Question

a velocity time graph for a particle in a straight line motion is given below the corresponding acceleration time graph will be

Answer 1

Explanation:

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.