Question

A car starts from rest, moves with an acceleration $a$ and then decelerates at $b$ for some time to come to rest. If the total time taken is $t$, the maximum velocity is

• A. $\frac{abt}{a+b}$
• B. $\frac{a^2}{a+b}$
• C. $\frac{at}{a+b}$
• D. $\frac{b^2}{a+b}$

Answer 1

The correct option is A $\frac{abt}{a+b}$

Let $t_1$ be the time for acceleration and $t-t_1$ be the time for deceleration and $v$ be maximum velocity.
$v=0+t_1\&0=v-b(t-t_1)\Rightarrow a{t}_1=b(t-t_1)\Rightarrow t_1=\frac{bt}{a+b}\Rightarrow v=\frac{abt}{a+b}$