A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

Let the car accelerate at rate α for time t1 Then maximum velocity attained, v=0+αt1+αt1Now, the car decelerates at a rate β for time (t - t1) and finally comes to rest. Then, 0=vβt−t1⇒0=αt1−βt+βt1⇒ t1=βα+βt∴ v=αβα+βt