Question

A body starting from rest accelerates at a constant rate of $am/s^2$ for some time after which it decelerates at a constant rate of $bm/s^2$ to come to rest finally. If the total time elapsed is $ts$, find the maximum velocity attained by the body.

Answer 1

Let the body accelerate for $t_{1}s$ and decelerate for $t_{2}s$.
At $t=t_1$, $v_{max}=0+a{t}_1$
$\Rightarrow t_1=\frac{v_{max}}{a}$
Similarly, $t_2=\frac{v_{max}}{b}$
Now, $t_1+t_2=\frac{v_{max}}{a}+\frac{v_{max}}{b}$
$\Rightarrow t=v_{max}(\frac{1}{a}+\frac{1}{b})$
$\therefore v_{max}=t\left(\frac{ab}{a+b}\right)$