Rekenen aan een (v,t)-diagram

Leerdoelen

Na deze les kun je:

•de gemiddelde versnelling bepalen uit een (v,t)-diagram.

•de versnelling op een bepaald momentbepalen uit een (v,t)-diagram.

•de gemiddelde snelheid bepalen uit een (v,t)-diagram.

•de verplaatsingbepalen uit een (v,t)-diagram.

•beargumenteren of een beweging eenparig versneld, eenparig vertraagd, versneld of vertraagd is aan de hand van een (v,t)-diagram.

De beweging in een (v,t)-diagram begrijpen

Een (v,t)-diagram (snelheid-tijd-diagram) is een grafiek die de snelheidvan een voorwerp uitzet tegen de tijd. De vorm van de grafiek vertelt je veel over het type beweging.

•Schuine rechte lijn: Dit duidt op een eenparig versnelde of eenparig vertraagde beweging. De snelheid verandert dan met een constante hoeveelheid per seconde.

•Als de lijn omhoog gaat, is de beweging versneld.

•Als de lijn omlaag gaat, is de beweging vertraagd.

•Horizontale lijn: Dit betekent dat de snelheid constant is. Er is dan geen versnelling.

•Kromme lijn: Dit geeft aan dat de versnelling niet constant is. De beweging is dan wel versneld of vertraagd, maar niet eenparig.

De steilheid van de grafiek in een (v,t)-diagram geeft de versnellinga\left(t\right)a\left(t\right)a\left(\right)aweer. Hoe steiler de lijn, hoe groter de versnelling (of vertraging).

De gemiddelde versnelling bepalen

De gemiddelde versnellinga_{gem}a_{ge}a_{g}a_{g}eis de verandering in snelheid\Delta v\Deltagedeeld door de verandering in tijd\Delta t\Delta. De formule hiervoor is:

a_{gem}=\frac{\Delta v}{\Delta t}a_{gem}=\frac{\Delta v}{\Delta t}/a_{gem}=\frac{\Delta v}{\Delta t}/\Deltaa_{gem}=\frac{\Delta v}{\Delta t}/\Delta Ta_{gem}=\frac{\Delta v}{\Delta}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{}/\Delta Ta_{gem}=\frac{\Delta v}{\placeholder{}}/\Delta Ta_{gem}=\Delta v/\Delta Ta_{gem}=\Delta v./\Delta Ta_{gem}=\Delta v/\Delta Ta_{gem}=\Delta/\Delta Ta_{gem}=\Delta V/\Delta Ta_{gem}=\Delta Vv/\Delta Ta_{gem}=\Delta V/\Delta Ta_{ge}=\Delta V/\Delta Ta_{g}=\Delta V/\Delta Ta_{g}e=\Delta V/\Delta Ta_{g}=\Delta V/\Delta Ta_{g}e=\Delta V/\Delta T

Bij een eenparig versnelde of vertraagde beweging (rechte lijn)

Als de grafiek een schuine rechte lijn is, is de versnelling constant en gelijk aan de gemiddelde versnelling over elk tijdsinterval.

Rekenvoorbeeld: Stel, je hebt een (v,t)-diagram zoals hierboven, met een stip opt=0\operatorname{s}t=0\operatorname{ms}t=0\operatorname{msm}t=0\operatorname{mm}t=0mt=0t=0\capt=0nt=0bijv=16\operatorname{m\/s}v=16\operatorname{m\/sm}v=16\operatorname{msm}v=16\operatorname{msm}v=16\operatorname{msm}v=16\operatorname{mm}v=16\operatorname{m\/sm}v=16\operatorname{m}v=16\operatorname{m\/}v=16\operatorname{m\/s}v=16\operatorname{m\/sm}v=16\operatorname{mm}v=16\operatorname{mm}v=16\operatorname{mm}v=16\operatorname{mm}v=16\operatorname{\frac{m}{\placeholder{}}m}v=16\operatorname{\frac{m}{s}m}v=16\operatorname{\frac{m}{\placeholder{}}m}v=16\operatorname{mm}v=16mv=16v=16nv=16v=16mv=16m/en een stip opt=3\operatorname{s}t=3\operatorname{sm}t=3\operatorname{smm}t=3\operatorname{mm}t=3mt=3bijv=10\operatorname{m\/s}v=10\operatorname{m\/sm}v=10\operatorname{msm}v=10\operatorname{msm}v=10\operatorname{msm}v=10\operatorname{mm}v=10mv=10v=10mv=10m/v=10m/s=10m/s.

•\Delta v=v_{eind}-v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=_{eind}-v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sZm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/m}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sZm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V=_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=v_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=v_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-v=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V=v_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V=_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/s}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{m\/sm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{msm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{msm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{msm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\operatorname{mm}\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6m\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6m\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6m/\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/s}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{m\/sm}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{msm}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{msm}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{msm}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16\operatorname{mm}=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16m=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16m=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16m/=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/s}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{m\/sm}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{msm}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{msm}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{msm}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10\operatorname{mm}-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10m-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10m-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10m/-16m/s=-6m/s\Delta v=V_{eind}-V_{begin}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{begifn}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{begif}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{begi}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{beg}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{be}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{b}=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{b}e=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{b}eg=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{b}egi=10m/s-16m/s=-6m/s\Delta v=V_{eind}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{eidnd}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{eidn}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{eid}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{ei}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e\in}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{ei}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e\in}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e\in d}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e\in}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{ei}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}i-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}in-V_{b}egin=10m/s-16m/s=-6m/s\Delta v=V_{e}ind-V_{b}egin=10m/s-16m/s=-6m/s\Delta=V_{e}ind-V_{b}egin=10m/s-16m/s=-6m/s

•\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3\operatorname{s}\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3\operatorname{sm}\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3\operatorname{msm}\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3\operatorname{mm}\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3m\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{s}=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{sm}=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{msm}=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0\operatorname{mm}=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0m=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{s}-0s=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{sm}-0s=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{msm}-0s=3s\Delta t=t_{eind}-t_{begin}=3\operatorname{mm}-0s=3s\Delta t=t_{eind}-t_{begin}=3m-0s=3s\Delta t=t_{eind}-t_{begin}=3-0s=3s\Delta t=t_{eind}-t_{begin}=3s-0s=3s\Delta=t_{eind}-t_{begin}=3s-0s=3s\Delta T=t_{eind}-t_{begin}=3s-0s=3s\Delta T=t_{eignd}-t_{begin}=3s-0s=3s\Delta T=t_{eign}-t_{begin}=3s-0s=3s\Delta T=t_{eig}-t_{begin}=3s-0s=3s\Delta T=t_{ei}-t_{begin}=3s-0s=3s\Delta T=t_{e}-t_{begin}=3s-0s=3s\Delta T=t_{e}i-t_{begin}=3s-0s=3s\Delta T=t_{e}in-t_{begin}=3s-0s=3s\Delta T=t_{e}ind-t_{begin}=3s-0s=3s\Delta T=t_{e}ind-t_{begign}=3s-0s=3s\Delta T=t_{e}ind-t_{begig}=3s-0s=3s\Delta T=t_{e}ind-t_{begi}=3s-0s=3s\Delta T=t_{e}ind-t_{beg}=3s-0s=3s\Delta T=t_{e}ind-t_{beg\in}=3s-0s=3s\Delta T=t_{e}ind-t_{begi}=3s-0s=3s\Delta T=t_{e}ind-t_{beg}=3s-0s=3s\Delta T=t_{e}ind-t_{be}=3s-0s=3s\Delta T=t_{e}ind-t_{b}=3s-0s=3s\Delta T=t_{e}ind-t_{b}e=3s-0s=3s\Delta T=t_{e}ind-t_{b}eg=3s-0s=3s\Delta T=t_{e}ind-t_{b}egi=3s-0s=3s

•a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{m\/s^2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{m\/s^2m}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{m\/s^2m}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{ms^2m}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{ms^2m}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{ms^2m}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{msm}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2\operatorname{mm}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2ma_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2ma_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2m/a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2m/sa_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2m/s^a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/s}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{m\/sm}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{msm}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{msm}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{msm}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6\operatorname{mm}}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6n}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3\operatorname{s}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3\operatorname{sm}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3\operatorname{msm}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3\operatorname{mm}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3m}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{3}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{6m/s}{\placeholder{}}=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-6m/s=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-6m/s/=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-6m/s/3=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta t}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{\Delta}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{}=-6m/s/3s=-2m/s^{2}a_{gem}=\frac{\Delta v}{\placeholder{}}=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta v=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta v/=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta v/\Delta=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta v/\Delta T=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta/\Delta T=-6m/s/3s=-2m/s^{2}a_{gem}=\Delta V/\Delta T=-6m/s/3s=-2m/s^{2}a_{ge}=\Delta V/\Delta T=-6m/s/3s=-2m/s^{2}a_{g}=\Delta V/\Delta T=-6m/s/3s=-2m/s^{2}a_{g}e=\Delta V/\Delta T=-6m/s/3s=-2m/s^{2}

De versnelling is hier-2\operatorname{m\/s^2}. Dit betekent dat de beweging een vertraging heeft van2\operatorname{m\/s^2}.

Bij een versnelde of vertraagde beweging (kromme lijn)

Als de grafiek een kromme lijn is, is de versnelling niet constant. Om de gemiddelde versnelling te bepalen tussen twee punten A en B, gebruik je een snijlijn. Een snijlijn is een rechte lijn die door twee punten op de kromme grafiek gaat. De steilheid van deze snijlijn geeft de gemiddelde versnelling tussen die twee punten weer.

Rekenvoorbeeld: Stel, je hebt een kromme grafiek en je wilt de gemiddelde versnelling bepalen tussen punt A (v=13\operatorname{m\/s}v=13v=1v-t-diagrammetkrommelijndievanV=13m/snaarV=0m/sgaat.EensnijlijnisgetekendtussenpuntA(beginvandekromme,V=13m/s)enpuntB(eindevandekromme,V=0m/sbijT=30ms)v=1v=13v=13mv=13m/) en punt B (v=0\operatorname{m\/s}v=0v=0mv=0m/v=0m/s=0m/sV=0m/sVv=0m/sopt=30\operatorname{ms}t=30\operatorname{msm}t=30\operatorname{mm}t=30\operatorname{mms}t=30\operatorname{mm}t=30mt=30t=30mt=30mst=30ms=t=30ms==t=30ms=).

•\Delta v=v_{eind}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta=v_{eind}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=v_{eind}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=_{eind}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{eind}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{eifnd}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{eifn}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{eif}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{ei}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}i-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}in-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-v_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begin}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begifn}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begif}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begi}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{beg}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begf}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begf\in}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begfi}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{begf}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{beg}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{be}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{bef}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{befg}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{befg}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{be}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}e=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}eg=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egi=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0\operatorname{m\/s}-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13\operatorname{m\/s}=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13m=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13m/=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13m/s=-13\operatorname{m\/s}\Delta V=V_{e}ind-V_{b}egin=0m/s-13m/s=-13\Delta V=V_{e}ind-V_{b}egin=0m/s-13m/s=-13m\Delta V=V_{e}ind-V_{b}egin=0m/s-13m/s=-13m/

•\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}\operatorname{s}\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}\operatorname{sm}\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}\operatorname{msm}\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}\operatorname{mm}\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}m\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-3}s\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-}s\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30\cdot10^{-}3s\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=3010^{-}3s\Delta t=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{eind}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{eifnd}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{eifn}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{eif}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{ei}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}i-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}in-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{begin}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{begifn}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{begif}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{begi}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{beg}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{be}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}e=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}eg=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egi=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30\operatorname{ms}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30\operatorname{msm}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30\operatorname{mm}-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30m-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30m-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0\operatorname{ms}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0\operatorname{msm}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0\operatorname{mm}=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0m=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0=30*10^{-}3s\Delta T=t_{e}ind-t_{b}egin=30ms-0m=30*10^{-}3s

•a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(3=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot1=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10^{}=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10^{-}=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10^{-3}=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10^{-3}\operatorname{s}=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{s}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{sm}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{msm}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}\operatorname{mm}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}m}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-3}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10^{-}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot10}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot1}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30\cdot}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{30}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{3}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13\operatorname{m\/s}}{\placeholder{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13}{\placeholder{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13m}{\placeholder{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13m/}{\placeholder{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-\frac{13m/s}{\placeholder{}}(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-13m/s(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta t}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\Delta}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\frac{\Delta v}{\placeholder{}}=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta v=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta v/=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta v/\Delta=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta v/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{gem}=\Delta V/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{ge}=\Delta V/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}=\Delta V/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}e=\Delta V/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30\cdot10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(3010^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-3}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3\operatorname{s})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3\operatorname{sm})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3\operatorname{msm})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3\operatorname{mm})=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3m)=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3)=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3s)=-433\operatorname{m\/s}^2a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3s)=-433\operatorname{m\/s}a_{g}em=\Delta V/\Delta T=-13m/s/(30*10^{-}3s)=-433

Dit betekent een gemiddelde vertraging van433\operatorname{m\/s}^2433\operatorname{m\/s}433433m433m/433m/s433m/s^.

De versnelling op een bepaald momentbepalen

De versnelling op een specifiek momentwordt ook wel de momentane versnelling genoemd.

Bij een eenparig versnelde of vertraagde beweging (rechte lijn)

Bij een schuine rechte lijn is de versnelling overal hetzelfde. De momentane versnelling op een bepaald tijdstip t is dan gelijk aan de gemiddelde versnelling over elk interval.

Rekenvoorbeeld: Als de grafiek door het punt\left(0\operatorname{s},0\operatorname{m\/s}\right)\left(0\operatorname{sm},0\operatorname{m\/s}\right)\left(0\operatorname{msm},0\operatorname{m\/s}\right)\left(0\operatorname{mm},0\operatorname{m\/s}\right)\left(0m,0\operatorname{m\/s}\right)\left(0,0\operatorname{m\/s}\right)\left(0s,0\operatorname{m\/s}\right)\left(0s,0\right)\left(0s,0m\right)\left(0s,0m/\right)\left(0s,0m/s\right)\left(0s,0m/s\right)en\left(4\operatorname{s},4\operatorname{m\/s}\right)\left(4\operatorname{sm},4\operatorname{m\/s}\right)\left(4\operatorname{msm},4\operatorname{m\/s}\right)\left(4\operatorname{mm},4\operatorname{m\/s}\right)\left(4m,4\operatorname{m\/s}\right)\left(4,4\operatorname{m\/s}\right)\left(4s,4\operatorname{m\/s}\right)\left(4s,4\right)\left(4s,4m\right)\left(4s,4m/\right)\left(4s,4m/s\right)\left(4s,4m/s\right)gaat, en je wilt de versnelling opt=4\operatorname{s}t=4\operatorname{sm}t=4\operatorname{msm}t=4\operatorname{mm}t=4mt=4(punt C) weten:

•\Delta v=4\operatorname{m\/s}-0\operatorname{m\/s}=4\operatorname{m\/s}\Delta v=4\operatorname{m\/s}-0\operatorname{m\/s}=4\Delta v=4\operatorname{m\/s}-0\operatorname{m\/s}=4m\Delta v=4\operatorname{m\/s}-0\operatorname{m\/s}=4m/\Delta v=4\operatorname{m\/s}-0\operatorname{m\/s}=4m/s\Delta v=4\operatorname{m\/s}-0=4m/s\Delta v=4\operatorname{m\/s}-0m=4m/s\Delta v=4\operatorname{m\/s}-0m/=4m/s\Delta v=4\operatorname{m\/s}-0m/s=4m/s\Delta v=4-0m/s=4m/s\Delta v=4m-0m/s=4m/s\Delta v=4m/-0m/s=4m/s\Delta v=4m/s-0m/s=4m/s\Delta=4m/s-0m/s=4m/s

•\Delta t=4\operatorname{s}-0\operatorname{s}=4\operatorname{s}\Delta t=4\operatorname{s}-0\operatorname{s}=4\operatorname{sm}\Delta t=4\operatorname{s}-0\operatorname{s}=4\operatorname{msm}\Delta t=4\operatorname{s}-0\operatorname{s}=4\operatorname{mm}\Delta t=4\operatorname{s}-0\operatorname{s}=4m\Delta t=4\operatorname{s}-0\operatorname{s}=4\Delta t=4\operatorname{s}-0\operatorname{s}=4s\Delta t=4\operatorname{s}-0\operatorname{sm}=4s\Delta t=4\operatorname{s}-0\operatorname{sm}=4s\Delta t=4\operatorname{s}-0\operatorname{m}=4s\Delta t=4\operatorname{s}-0\operatorname{sm}=4s\Delta t=4\operatorname{s}-0\operatorname{msm}=4s\Delta t=4\operatorname{s}-0\operatorname{mm}=4s\Delta t=4\operatorname{s}-0m=4s\Delta t=4\operatorname{s}-0=4s\Delta t=4\operatorname{s}-0s=4s\Delta t=4\operatorname{sm}-0s=4s\Delta t=4\operatorname{msm}-0s=4s\Delta t=4\operatorname{mm}-0s=4s\Delta t=4m-0s=4s\Delta t=4-0s=4s\Delta t=4s-0s=4s\Delta=4s-0s=4s

•a_{gem}=a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2a_{gem}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2a_{ge}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2a_{g}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2aa=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}^2a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1\operatorname{m\/s}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1ma=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1m/a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1m/sa=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1m/s^a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{s}}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{sm}}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{msm}}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4\operatorname{mm}}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4m}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{4}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=\frac{4\operatorname{m\/s}}{\placeholder{}}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4\operatorname{m\/s}=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m/=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m/s=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m/s/=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m/s/4=1m/s^{2}a=\frac{\Delta v}{\Delta t}=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{\Delta t}/=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{\Delta t}/\Delta=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{\Delta t}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{\Delta}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{}/\Delta T=4m/s/4s=1m/s^{2}a=\frac{\Delta v}{\placeholder{}}/\Delta T=4m/s/4s=1m/s^{2}a=\Delta v/\Delta T=4m/s/4s=1m/s^{2}a=\Delta/\Delta T=4m/s/4s=1m/s^{2}

Bij een versnelde of vertraagde beweging (kromme lijn)

Bij een kromme lijn verandert de versnelling continu. Om de momentane versnelling op een specifiek tijdstip T te bepalen, teken je een raaklijn aan de grafiek in dat punt. Een raaklijn is een rechte lijn die de kromme grafiek precies op één punt raakt en dezelfde steilheid heeft als de grafiek op dat punt. De steilheid van deze raaklijn geeft de momentane versnelling weer.

Rekenvoorbeeld: Stel, je hebt een kromme grafiek en je wilt de versnelling op tijdstipt=25\operatorname{ms}t=25\operatorname{msm}t=25\operatorname{mm}t=25mt=25t=25m(punt C) weten. Je tekent een raaklijn in punt C. Deze raaklijn loopt bijvoorbeeld vanv=16\operatorname{m\/s}v=16v=16mv=16m/v=16m/s=16m/snaarv=0\operatorname{m\/s}v=0v=0mv=0m/v=0m/s=0m/sover een tijdsinterval van20\operatorname{ms}20\operatorname{msm}20\operatorname{mm}20m2020m.

•\Delta v=v_{eind\,raaklijn}-v_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta=v_{eind\,raaklijn}-v_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=v_{eind\,raaklijn}-v_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=_{eind\,raaklijn}-v_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklijn}-v_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklijn}-_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklijn}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklijnb}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklijn}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaklij}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raakli}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raakl}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raak}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaki}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raakij}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raakijn}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raakij}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raaki}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raak}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,raa}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,ra}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,r}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind\,}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eind}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eidnd}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eidn}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eidnd}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eidn}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{eid}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{ei}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}i-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}in-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}a-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aa-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aak-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aakl-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aakli-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklij-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\,raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{beginraaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{beginraaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{beginraaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raaklijn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raaklij}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raakli}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raakl}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raak}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_raa}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_ra}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_r}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin\_}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{r}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,r}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,ra}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,raa}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,raak}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,raa}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,ra}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,r}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin,}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begin}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begifn}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begif}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begifi}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begif}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{begi}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{beg}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{be}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}e=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}eg=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egi=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}a=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aa=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aak=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aakl=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aakli=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklij=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0\operatorname{m\/s}-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16\operatorname{m\/s}=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m/=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m/s=-16\operatorname{m\/s}\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m/s=-16\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m/s=-16m\Delta V=V_{e}ind_{r}aaklijn-V_{b}egin_{r}aaklijn=0m/s-16m/s=-16m/

•\Delta t=t_{eind\,raaklijn}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta=t_{eind\,raaklijn}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raaklijn}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raaklij}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raakli}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raakl}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raak}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,raa}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,ra}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,r}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind\,}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eind}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eifnd}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eifn}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{eif}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{ei}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}i-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}in-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}a-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aa-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aak-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aakl-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aakli-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklij-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raaklijn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raaklij}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raakli}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raakl}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raak}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,raa}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,ra}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,r}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin\,}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begin}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begixn}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begix}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{begi}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{beg}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{be}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}e=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}eg=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egi=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}a=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aa=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aak=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aakl=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aakli=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklij=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20\operatorname{ms}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20\operatorname{msm}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20\operatorname{mm}=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20m=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20m=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20\cdot10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=2010^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-3}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3\operatorname{s}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3\operatorname{sm}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3\operatorname{msm}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3\operatorname{mm}\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3m\Delta T=t_{e}ind_{r}aaklijn-t_{b}egin_{r}aaklijn=20ms=20*10^{-}3

•a=\left(\frac{\Delta v}{\Delta t}\right)_{raaklijn}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{raaklij}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{raakli}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{raakl}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{raak}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{raa}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{ra}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)_{r}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}\right)=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\left(\frac{\Delta v}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2\right)a=\frac{\Delta v}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta Vv}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{\Delta t}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{\Delta}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\frac{\Delta V}{\placeholder{}}=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/\Delta=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/\Delta t=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/\Delta=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(2=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot1=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10^{}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10^{-}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10^{-3}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10^{-3}\operatorname{s}=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{s}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{sm}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{msm}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}\operatorname{mm}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}m}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-3}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10^{-}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot10}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot1}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20\cdot}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{20}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{2}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-\frac{16\operatorname{m\/s}}{\placeholder{}}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16\operatorname{m\/s}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16\operatorname{m\/s}./(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16\operatorname{m\/s}/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m//(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20\cdot10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(2010^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-3}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3\operatorname{s})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3\operatorname{ms})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3\operatorname{msm})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3\operatorname{mm})=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3m)=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3)=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800\operatorname{m\/s}^2a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800\operatorname{m\/s}a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800ma=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800m/a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800m/sa=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800m/s^a=\Delta V/\Delta T=-16m/s/(20*10^{-}3s)=-800m/s^{}

In dit voorbeeld is de vertraging op dat moment800\operatorname{m\/s}^2800\operatorname{m\/s}800800m800m/800m/s800m/s^. Dit punt C is overigens het punt waar de vertraging maximaal is, omdat de grafiek daar het steilst omlaag gaat.

De gemiddelde snelheid bepalen

Bij een eenparig versnelde of vertraagde beweging (rechte lijn)

Voor een beweging met een constante versnelling (eenparig versneld of vertraagd, dus een rechte lijn in het (v,t)-diagram), kun je de gemiddelde snelheid (v_{gem}v_{ge}v_{g}v_{g}e) eenvoudig berekenen met de formule:

v_{gem}=\frac{(v_{begin}+v_{eind})}{2}v_{gem}=\frac{(v_{begin}+v_{eind})}{\placeholder{}}v_{gem}=(v_{begin}+v_{eind})v_{gem}=(v_{begin}+v_{eind})/v_{gem}=(v_{begin}+v_{eind})/2v_{gem}=(v_{begin}+v_{eifnd})/2v_{gem}=(v_{begin}+v_{eifn})/2v_{gem}=(v_{begin}+v_{eif})/2v_{gem}=(v_{begin}+v_{ei})/2v_{gem}=(v_{begin}+v_{e})/2v_{gem}=(v_{begin}+v_{e}i)/2v_{gem}=(v_{begin}+v_{e}in)/2v_{gem}=(v_{begin}+v_{e}ind)/2v_{gem}=(v_{begin}+_{e}ind)/2v_{gem}=(v_{begin}+V_{e}ind)/2v_{gem}=(v_{begixn}+V_{e}ind)/2v_{gem}=(v_{begix}+V_{e}ind)/2v_{gem}=(v_{begi}+V_{e}ind)/2v_{gem}=(v_{beg}+V_{e}ind)/2v_{gem}=(v_{be}+V_{e}ind)/2v_{gem}=(v_{b}+V_{e}ind)/2v_{gem}=(v+V_{e}ind)/2v_{gem}=(+V_{e}ind)/2v_{gem}=(V+V_{e}ind)/2v_{gem}=(+V_{e}ind)/2v_{gem}=(V+V_{e}ind)/2v_{gem}=(V_{}+V_{e}ind)/2v_{gem}=(V_{b}+V_{e}ind)/2v_{gem}=(V_{b}e+V_{e}ind)/2v_{gem}=(V_{b}eg+V_{e}ind)/2v_{gem}=(V_{b}egi+V_{e}ind)/2v_{gem}=(V_{b}egin+V_{e}ind)/2v_{ge}=(V_{b}egin+V_{e}ind)/2v_{g}=(V_{b}egin+V_{e}ind)/2v_{g}e=(V_{b}egin+V_{e}ind)/2

Deze formule geldt alleen voor bewegingen met een constante versnelling!

Je kunt dit ook grafisch controleren: als je een horizontale lijn tekent op de hoogte van de gemiddelde snelheid, dan moeten de oppervlaktes die boven en onder deze lijn liggen en begrensd worden door de oorspronkelijke grafiek, even groot zijn.

Bij een versnelde of vertraagde beweging (kromme lijn) - de oppervlaktemethode

Als de grafiek een kromme lijn is, kun je de formulev_{gem}=\frac{(v_{begin}+v_{eind})}{2}v_{gem}=\frac{(v_{begin}+v_{eind})}{\placeholder{}}v_{gem}=(v_{begin}+v_{eind})v_{gem}=(v_{begin}+v_{eind})/v_{gem}=(v_{begin}+v_{eind})/2v_{gem}=(v_{begin}+v_{eifnd})/2v_{gem}=(v_{begin}+v_{eifn})/2v_{gem}=(v_{begin}+v_{eif})/2v_{gem}=(v_{begin}+v_{ei})/2v_{gem}=(v_{begin}+v_{e})/2v_{gem}=(v_{begin}+v_{e}i)/2v_{gem}=(v_{begin}+v_{e}in)/2v_{gem}=(v_{begin}+v_{e}ind)/2v_{gem}=(v_{begin}+_{e}ind)/2v_{gem}=(v_{begin}+V_{e}ind)/2v_{gem}=(v_{begixn}+V_{e}ind)/2v_{gem}=(v_{begix}+V_{e}ind)/2v_{gem}=(v_{begi}+V_{e}ind)/2v_{gem}=(v_{beg}+V_{e}ind)/2v_{gem}=(v_{be}+V_{e}ind)/2v_{gem}=(v_{b}+V_{e}ind)/2v_{gem}=(v_{b}e+V_{e}ind)/2v_{gem}=(v_{b}eg+V_{e}ind)/2v_{gem}=(v_{b}egi+V_{e}ind)/2v_{gem}=(v_{b}egin+V_{e}ind)/2v_{gem}=(_{b}egin+V_{e}ind)/2v_{gem}=(v_{b}egin+V_{e}ind)/2v_{gem}=(_{b}egin+V_{e}ind)/2v_{gem}=(V_{b}egin+V_{e}ind)/2v_{ge}=(V_{b}egin+V_{e}ind)/2v_{g}=(V_{b}egin+V_{e}ind)/2v_{g}e=(V_{b}egin+V_{e}ind)/2niet gebruiken. Je moet de gemiddelde snelheid dan grafisch schatten met behulp van de oppervlaktemethode.

1.Schat de hoogte: Teken een horizontale lijn in het (v,t)-diagram waarvan je denkt dat deze de gemiddelde snelheid voorstelt.

2.Controleer de oppervlaktes: Controleer of de oppervlakte die boven de geschatte lijn ligt en onder de grafiek, gelijk is aan de oppervlakte die onder de geschatte lijn ligt en boven de grafiek. Als deze oppervlaktes gelijk zijn, heb je de gemiddelde snelheid goed geschat.

De verplaatsingbepalen

De verplaatsing(of afgelegde weg) van een voorwerp kan worden bepaald door de oppervlakte onder het (v,t)-diagram te berekenen. Dit komt omdats=v\cdot ts=v\cdots=vs=s=Vs=V*s=V*T=V*TS=V*TSs=V*T. In een (v,t)-diagram is de 'hoogte' de snelheidven de 'breedte' de tijdt. Het product hiervan is de oppervlakte, en die oppervlakte staat gelijk aan de verplaatsing.

Door op te delen in rechthoeken en driehoeken

Bij complexe (v,t)-diagrammen kun je de oppervlakte onder de grafiek opdelen in eenvoudige geometrische vormen zoals rechthoeken en driehoeken. Bereken de oppervlakte van elk deel en tel deze bij elkaar op om de totale verplaatsing te vinden.

Rekenvoorbeeld: Stel, je hebt een (v,t)-diagram dat is opgedeeld in vier vlakken:

•Oppervlakte 1 (driehoek):0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot h=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot ho=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot hoo=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot hoog=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot hoogt=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot b\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot ba\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot bas\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot basi\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5\cdot basis\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5basis\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5*basis\cdot hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5*basishoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5\cdot1\operatorname{s}\cdot\,4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5\cdot1\operatorname{s}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5\cdot1\operatorname{s}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5\cdot1\operatorname{s}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.51\operatorname{s}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{s}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{sm}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{msm}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{mm}\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1m\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s\cdot4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4m=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4m/=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4m/s=2\operatorname{m}0.5*basis*hoogte=0.5*1s*4m/s=2\operatorname{mm}0.5*basis*hoogte=0.5*1s*4m/s=2m0.5*basis*hoogte=0.5*1s*4m/s=2

•Oppervlakte 2 (rechthoek):\text{basis}\,\cdot\,\text{hoogte}=3\operatorname{s}\cdot\,4\operatorname{m\/s}=12\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=3\operatorname{s}\cdot\,4\operatorname{m\/s}=1\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=3\operatorname{s}\cdot\,4\operatorname{m\/s}=\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=3\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,3\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=4\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{m}\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot\,4\operatorname{m\/s}=4\operatorname{mm}\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot\,4\operatorname{m\/s}=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot\,4\operatorname{m\/s}=4\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot\,4\operatorname{m\/s}=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4\operatorname{m\/s}=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4\operatorname{m\/s}=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4\operatorname{m\/s}=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4m=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4m/=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{s}\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{sm}\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{msm}\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1\operatorname{mm}\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1m\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1s\cdot4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1s4m/s=4m\text{basis}\,\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis}\,\cdot\text{hoogte}=1s*4m/s=4m\text{basis}\,\cdot\text{hoogte}=1s*4m/s=4m\text{basis}\,\cdot\text{hoogte}=1s*4m/s=4m\text{basis}\,\cdot\text{hoogte}=1s*4m/s=4m\text{basis}\,\cdot\text{hoogte}=1s*4m/s=4m\text{basis}\,\text{hoogte}=1s*4m/s=4m\text{basis\textasteriskcentered}\,\text{hoogte}=1s*4m/s=4m\text{basis}\,\text{hoogte}=1s*4m/s=4m\text{basis}\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis\textbackslash}\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis\textbackslash,}\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis\textbackslash,}\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis\textbackslash}\cdot\,\text{hoogte}=1s*4m/s=4m\text{basis}\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4m\cdot\,\text{hoogte}=1s*4m/s=4mb\cdot\,\text{hoogte}=1s*4m/s=4mba\cdot\,\text{hoogte}=1s*4m/s=4mbas\cdot\,\text{hoogte}=1s*4m/s=4mbasi\cdot\,\text{hoogte}=1s*4m/s=4mbasis\cdot\,\text{hoogte}=1s*4m/s=4mbasis\cdot\text{hoogte}=1s*4m/s=4mbasis\cdot\text{hoogte}=1s*4m/s=4mbasis\cdot\text{hoogte}=1s*4m/s=4mbasis\text{hoogte}=1s*4m/s=4mbasis*\text{hoogte}=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*=1s*4m/s=4mbasis*h=1s*4m/s=4mbasis*ho=1s*4m/s=4mbasis*hoo=1s*4m/s=4mbasis*hoog=1s*4m/s=4mbasis*hoogt=1s*4m/s=4m(vant=1\operatorname{s}t=1\operatorname{sm}t=1\operatorname{msm}t=1\operatorname{mm}t=1mt=1tott=2\operatorname{s}t=2\operatorname{sm}t=2\operatorname{msm}t=2\operatorname{mm}t=2mt=2,v=4\operatorname{m\/s}=4\operatorname{m\/s}V=4\operatorname{m\/s}V=4V=4mV=4m/)

•Oppervlakte 3 (driehoek):0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot(8-4)\operatorname{m\/s}=4\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot(8-4)\operatorname{m\/s}=\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot\text{hoogte}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot\text{basis}=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5\cdot=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*b=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*ba=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*bas=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basi=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*h=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*ho=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoo=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoog=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogt=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5\cdot1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.51\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{s}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{sm}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{msm}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\operatorname{mm}\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1m\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s\cdot(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)\operatorname{m\/s}=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)m=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)m/=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)m/s=2\operatorname{m}0.5*basis*hoogte=0.5*1s*(8-4)m/s=2\operatorname{mm}0.5*basis*hoogte=0.5*1s*(8-4)m/s=2m0.5*basis*hoogte=0.5*1s*(8-4)m/s=2(vant=2\operatorname{s}t=2\operatorname{sm}t=2\operatorname{msm}t=2\operatorname{mm}t=2mt=2tott=3\operatorname{s}t=3\operatorname{sm}t=3\operatorname{msm}t=3\operatorname{mm}t=3mt=3,vvannaar8\operatorname{m\/s}88m8m/)

•Oppervlakte 4 (driehoek):0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,8\operatorname{m\/s}=4\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,8\operatorname{m\/s}=\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot1\operatorname{s}\cdot\,8\operatorname{m\/s}=8\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot\operatorname{s}\cdot\,8\operatorname{m\/s}=8\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot\,8\operatorname{m\/s}=8\operatorname{m}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot\,8\operatorname{m\/s}=8\operatorname{mm}0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot\,8\operatorname{m\/s}=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot\,8\operatorname{m\/s}=80.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot\,8\operatorname{m\/s}=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8\operatorname{m\/s}=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8\operatorname{m\/s}=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8\operatorname{m\/s}=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8m=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8m/=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}\cdot8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{s}*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{sm}*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{msm}*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2\operatorname{mm}*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2m*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5\cdot2s*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.52s*8m/s=8m0.5\cdot\,\text{basis}\cdot\,\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\,\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\,\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\,\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot\text{hoogte}=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}\cdot=0.5*2s*8m/s=8m0.5\cdot\text{basis}=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5\cdot=0.5*2s*8m/s=8m0.5=0.5*2s*8m/s=8m0.5*=0.5*2s*8m/s=8m0.5*b=0.5*2s*8m/s=8m0.5*ba=0.5*2s*8m/s=8m0.5*bas=0.5*2s*8m/s=8m0.5*basi=0.5*2s*8m/s=8m0.5*basis=0.5*2s*8m/s=8m0.5*basis*=0.5*2s*8m/s=8m0.5*basis*h=0.5*2s*8m/s=8m0.5*basis*ho=0.5*2s*8m/s=8m0.5*basis*hoo=0.5*2s*8m/s=8m0.5*basis*hoog=0.5*2s*8m/s=8m0.5*basis*hoogt=0.5*2s*8m/s=8m(vant=3\operatorname{s}t=3\operatorname{sm}t=3\operatorname{msm}t=3\operatorname{mm}t=3mt=3t=3\capt=3nt=3tott=5\operatorname{s}t=5\operatorname{sm}t=5\operatorname{msm}t=5\operatorname{mm}t=5mt=5t=5\capt=5nt=5,vvannaar0\operatorname{m\/s}00m0m/)

De totale verplaatsingvan de beweging is de som van de oppervlaktes: s_{totaal}=s_{totaa}=s_{tota}=s_{tot}=s_{to}=s_{t}=s_{}=s_{r}=s_{}=s_{t}=s_{t\lor}=s_{t\lor a}=s_{t\lor aa}=s_{t\lor a}=s_{t\lor}=s_{to}=s_{t}=s_{t}o=s_{t}ot=s_{t}ota=s_{t}otaa=s_{t}otaal=_{t}otaal=Oppervlakte 1 + Oppervlakte 2 + Oppervlakte 3 + Oppervlakte 4=2+12+4+4=22=2+12+4+=22=2+12+4=22=2+12+=22=2+12=22=2+1=22=2+=22=2=22==22=2=22=2+=22=2=22=2=22==22meter

Check met gemiddelde snelheid

Je kunt de berekende verplaatsing controleren door de gemiddelde snelheid te berekenen en deze grafisch te vergelijken.

•v_{gem}=\frac{s_{totaal}}{t_{totaal}}v_{gem}=\frac{s_{totaal}}{t_{totaal}}_{}v_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}v_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}ov_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}otv_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}otav_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}otaav_{gem}=\frac{s_{totaal}}{t_{totaal}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{totaa}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{tota}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{tot}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{to}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{toa}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{toaa}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{toaal}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{toaa}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{toa}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{to}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t_{t}}_{t}otaalv_{gem}=\frac{s_{totaal}}{t}_{t}otaalv_{gem}=\frac{s_{totaal}}{\placeholder{}}_{t}otaalv_{gem}=s_{totaal}_{t}otaalv_{gem}=s_{totaal}._{t}otaalv_{gem}=s_{totaal}_{t}otaalv_{gem}=s_{totaal}/_{t}otaalv_{gem}=s_{totaal}/T_{t}otaalv_{gem}=s_{totaa}/T_{t}otaalv_{gem}=s_{tota}/T_{t}otaalv_{gem}=s_{tot}/T_{t}otaalv_{gem}=s_{to}/T_{t}otaalv_{gem}=s_{t}/T_{t}otaalv_{gem}=s_{t}o/T_{t}otaalv_{gem}=s_{t}ot/T_{t}otaalv_{gem}=s_{t}ota/T_{t}otaalv_{gem}=s_{t}otaa/T_{t}otaalv_{gem}=s_{t}otaal/T_{t}otaalv_{gem}=_{t}otaal/T_{t}otaalv_{gem}=S_{t}otaal/T_{t}otaalv_{ge}=S_{t}otaal/T_{t}otaalv_{g}=S_{t}otaal/T_{t}otaalv_{g}e=S_{t}otaal/T_{t}otaal

•Alss_{totaal}=22\operatorname{m}s_{totaal}=22\operatorname{mm}s_{totaal}=22ms_{totaal}=22s_{totaal}=22ms_{totaal}=2ms_{totaal}=22ms_{tovtaal}=22ms_{tovtaa}=22ms_{tovta}=22ms_{tovt}=22ms_{tov}=22ms_{tovr}=22ms_{tovra}=22ms_{tovraa}=22ms_{tovraal}=22ms_{tovraa}=22ms_{tovra}=22ms_{tovr}=22ms_{tov}=22ms_{to}=22ms_{t}=22ms_{t\circ}=22ms_{t\circ r}=22ms_{t\circ}=22ms_{to}=22ms_{t}=22ms_{t\lor}=22ms_{to}=22ms_{t}=22ms_{t\lor}=22ms_{t\lor o}=22ms_{t\lor}=22ms_{}=22ms_{t}=22ms_{to}=22ms_{t}=22ms_{t\lor}=22ms_{t\lor a}=22ms_{t\lor aa}=22ms_{t\lor aal}=22ms_{t\lor aa}=22ms_{t\lor a}=22ms_{t\lor}=22ms_{to}=22ms_{t}=22ms_{t\lor}=22ms_{t\lor a}=22ms_{t\lor}=22ms_{to}=22ms_{t}=22ms_{t\lor}=22ms_{to}=22ms_{t}=22ms_{t}o=22ms_{t}ot=22ms_{t}ota=22ms_{t}otaa=22ms_{t}otaal=22m_{t}otaal=22mS_{t}otaal=22mS=_{t}otaal=22mS=s_{t}otaal=22mS=_{t}otaal=22ment_{totaal}=5\operatorname{s}t_{totaal}=5\operatorname{sm}t_{totaal}=5\operatorname{msm}t_{totaal}=5\operatorname{mm}t_{totaal}=5mt_{totaal}=5t_{totaal}=5st_{totaa}=5st_{tota}=5st_{tot}=5st_{to}=5st_{t}=5st_{t}o=5st_{t}ot=5st_{t}ota=5st_{t}otaa=5st_{t}otaal=5s_{t}otaal=5s, dan isv_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4{,}4\operatorname{m\/s}v_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=44\operatorname{m\/s}v_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4.4\operatorname{m\/s}v_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4.4v_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4.4mv_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4.4m/v_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}5=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5\operatorname{s}}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5\operatorname{sm}}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5\operatorname{msm}}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5\operatorname{mm}}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5m}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{5}5s=4.4m/sv_{gem}=\frac{22\operatorname{m}}{\placeholder{}}5s=4.4m/sv_{gem}=22\operatorname{m}5s=4.4m/sv_{gem}=22\operatorname{m}/5s=4.4m/sv_{gem}=22\operatorname{mm}/5s=4.4m/sv_{gem}=22m/5s=4.4m/sv_{gem}=22/5s=4.4m/sv_{gem}=22m/5s=4.4m/sv_{ge}=22m/5s=4.4m/sv_{gen}=22m/5s=4.4m/sv_{ge}=22m/5s=4.4m/sv_{g}=22m/5s=4.4m/sv_{g}e=22m/5s=4.4m/s.

Als je een horizontale lijn tekent opv=4{,}4\operatorname{m\/s}=4{,}4\operatorname{m\/s}V=4{,}4\operatorname{m\/s}V=44\operatorname{m\/s}V=4.4\operatorname{m\/s}V=4.4V=4.4mV=4.4m/, dan moeten de oppervlaktes boven en onder deze lijn (begrensd door de oorspronkelijke grafiek) ongeveer gelijk zijn.

Overzicht (x,t)- en (v,t)-diagram

Vergelijking met (x,t)-diagram

Ter herinnering:

•In een (x,t)-diagram (plaats-tijd-diagram) stelt de steilheid de snelheid voor. Je kunt hieruit de gemiddelde snelheid bepalen met een snijlijn en de snelheid op een bepaald tijdstip T met een raaklijn.

(v,t)-diagram

In een (v,t)-diagram:

•De steilheid stelt de versnelling voor.

•De oppervlakte onder de grafiek komt overeen met de verplaatsing(of).

Met een (v,t)-diagram kun je:

•De gemiddelde versnelling bepalen met een snijlijn.

•De versnelling op een bepaald tijdstiptbepalen met een raaklijn.

•De gemiddelde snelheid bepalen met een geschatte lijn door middel van de oppervlaktemethode.

•De verplaatsingsbepalen met behulp van de oppervlakte onder de grafiek.

Toepassing: de remmende auto

De startvraag was: wat voor beweging zie je in het diagram hiernaast en waarbij past deze beweging in het echte leven?

Dit diagram toont de beweging van een remmende auto.

1.Reactietijd: Eerst zie je een stukje met constante snelheid (bijvoorbeeldv=100\operatorname{km\/u}v=10\operatorname{km\/u}=10\operatorname{km\/u}V=10\operatorname{km\/u}V=10\operatorname{km\/um}V=10\operatorname{kmum}V=10\operatorname{kmum}V=10\operatorname{kmum}V=10\operatorname{kmm}V=10\operatorname{km}V=10kV=10V=100V=100\operatorname{\operatorname{km}\/s}V=100\operatorname{k\/s}V=100\operatorname{\/s}V=100\operatorname{m\/s}V=100V=100kV=100kmV=100km/, wat ongeveer27\operatorname{m\/s}2727m27m/is). Dit is de reactietijd van de bestuurder, waarin de auto nog met constante snelheid doorrijdt voordat de remmen worden ingetrapt.

1.De reactieafstand is de oppervlakte onder dit horizontale deel. Als de reactietijd 1 seconde is:s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1\operatorname{s}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1\operatorname{sm}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1\operatorname{msm}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1\operatorname{mm}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1m=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1{,}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1{,}{,}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1{,}=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,1=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,s=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot\,=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot1=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot1=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot1s=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot s=27s_{reactie}=v\cdot t=27\operatorname{m\/s}\cdot1s=27s_{reactie}=v\cdot t=27\operatorname{m\/s}1s=27s_{reactie}=v\cdot t=27\operatorname{m\/s}*1s=27s_{reactie}=v\cdot t=27*1s=27s_{reactie}=v\cdot t=27m*1s=27s_{reactie}=v\cdot t=27m/*1s=27s_{reactie}=v\cdot t=27m/s*1s=27s_{reactie}=v\cdot=27m/s*1s=27s_{reactie}=v=27m/s*1s=27s_{reactie}==27m/s*1s=27s_{reactie}=V=27m/s*1s=27s_{reactie}=V*=27m/s*1s=27s_{reactie}=V*T=27m/s*1s=27_{reactie}=V*T=27m/s*1s=27S_{reactie}=V*T=27m/s*1s=27S_{reacti}=V*T=27m/s*1s=27S_{react}=V*T=27m/s*1s=27S_{reac}=V*T=27m/s*1s=27S_{rea}=V*T=27m/s*1s=27S_{re}=V*T=27m/s*1s=27S_{r}=V*T=27m/s*1s=27S_{r}e=V*T=27m/s*1s=27S_{r}ea=V*T=27m/s*1s=27S_{r}eac=V*T=27m/s*1s=27S_{r}eact=V*T=27m/s*1s=27S_{r}eacti=V*T=27m/s*1s=27meter.

2.Remmen: Daarna volgt een eenparig vertraagde beweging, waarbij de snelheid snel afneemt. Dit is het moment dat de auto daadwerkelijk remt.

1.De remafstand is de oppervlakte onder dit schuine gedeelte (een driehoek). Als de vertraging11\operatorname{m\/s}^211\operatorname{m\/s}1111m11m/11m/s11m/s^is en het remmen2{,}5\operatorname{s}2{,}5\operatorname{sm}2{,}5\operatorname{msm}2{,}5\operatorname{mm}2{,}5\operatorname{mm}2{,}52{,}5\operatorname{mm}2{,}5m2{,}52{,}5s25s2n5s25sduurt:s_{rem}=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75_{rem}=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{rem}=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{re}=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}e=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0{,}5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=05\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5\cdot v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*v_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{begin}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{begixn}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{begix}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{begi}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{beg}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{be}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}e\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}eg\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egi\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin\cdot\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin\left(\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75\right)S_{r}em=0.5*V_{b}egin\left(\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75\right)S_{r}em=0.5*V_{b}egin\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta t=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0{,}5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=05\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5\cdot27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.527\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27\operatorname{m\/s}\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s\cdot2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2{,}5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*25\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5\operatorname{s}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5\operatorname{sm}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5\operatorname{msm}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5\operatorname{mm}=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5m=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5s=33{,}75S_{r}em=0.5*V_{b}egin*\Delta T=0.5*27m/s*2.5s=3375meter.

De totale stopafstand is de som van de reactieafstand en de remafstand. s_{stop}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{m}=60{,}75\operatorname{m}\thickapprox61s_{s\,top}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{m}=60{,}75\operatorname{m}\thickapprox61s_{s\,top}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{m}\thickapprox61s_{s\,top}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61_{s\,top}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s\,top}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s\,to}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s\,t}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s\,}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}t=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}to=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=s_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{reactie}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{reacti}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{react}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{reac}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{reaci}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{reac}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{rea}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{re}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}e+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}ea+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eac+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eact+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eacti+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+s_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{rem}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{re}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}e=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27\operatorname{m}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27\operatorname{mm}+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33{,}75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+3375\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75\operatorname{mm}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}m=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}mm=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}m=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}{,}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75{,}=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=60{,}75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=6075\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=60.75\operatorname{mm}\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=60.75m\thickapprox61S_{s}top=S_{r}eactie+S_{r}em=27m+33.75m=60.75\thickapprox61meter.