A car starts from rest and moves with uniform acceleration a on a straight road from t=0 to t=T. After that, constant deceleration brings it to rest. In this process the average speed of the car is:
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Question

A car starts from rest and moves with uniform acceleration a on a straight road from t=0 to t=T. After that, constant deceleration brings it to rest. In this process the average speed of the car is:

G1 Physics · Accepted Answer

The speed-time graph consists of acceleration from 0 to maximum speed=aT and then deceleration to 0. For any triangular v-t graph with zero speed at both ends, average speed = area/base = (1/2)(total time)(maximum speed)/(total time)=maximum speed/2=aT/2. Hence option C.