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Question

Velocity-time graph of a particle moving in a straight line is shown in figure. At time t=0, s=-10m. Plot corresponding a-t and s-t graphs.
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Solution

at t=0 S = -10m and V= 0
For acceleration time graph
a=dV/dt
or it may called as slope of v-t curve
hence plot the a-t curve
for first 2 sec
velocity is increasing constantly
slope is 10/2 = 5m/s^2 =a for first 2 sec
then for time t=2 to t= 4 velocity is constant hence no change in velocity slope is zero hence acceleration is zero
for next time t=4 to t= 8 velocity decreases linearly from 10 to -10 hence slope is -20/4 is -5m/s^2 = a (acceleration)
fot time t=8 to t=10 velocity increase from -10 to 0
slope is 10/2 = 5m/s^2

Same for s- t curve
v= ds/dt
ds = vdt
for first 2 sec from t=0 to t= 2 sec
s = -10 to 0
for next t=2 to t=4 seconds
s=0 to 20 m
for next t=4 to t=8
s=20 to 30m
similary we do for all time interval and we draw the curve a-t and s-t curves.

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