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

Let the car accelerate at the rate x for a time t1. The velocity will be maximum at time t2 . The velocity is given byv=0+at1=at1Now, the car decelerates at a rate of b for time (t - t1) and finally comes to rest. Therefore,0=v−bt−t1=at1−bt+bt1∴t1=ba+btSo, v=aba+bt