Question

A car accelerates from rest at a constant rate "a" for some time, after which it decelerates at a constant rate "b" and comes to rest. If the total time elapsed is "t", what will be the maximum velocity acquired by the car?

Answer 1

$v=u+at\Rightarrow u=at$ for time T and U = 0.
For time (t-T); if t is the total time, v = 0
$\Rightarrow 0=aT-b(t-T)\Rightarrow aT=-bt+bT\Rightarrow bt=(b-a)T\Rightarrow T=\frac{b}{(b-a)}t$
Maximum velocity $=aT=\frac{ab}{b-a}t\therefore \frac{ab}{b-a}t$.