First slide
Instantaneous acceleration
Question

A car starts from rest, moves with an acceleration a and then decelerates at a constant rate b for some time to come to rest. It the total time taken is f, the maximum velocity of car is given by

Difficult
Solution

Let the car accelerate at the rate x for a time t1. The velocity will be maximum at time t2 . The velocity is given by
v=0+at1=at1
Now, the car decelerates at a rate of b for time (t - t1) and finally comes to rest. Therefore,
0=vbtt1=at1bt+bt1t1=ba+bt
So, v=aba+bt

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