Question

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

• A. $\left(\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }\right)t$
• B. $\left(\frac{{\alpha }^2-{\beta }^2}{\alpha \beta }\right)t$
• C. None of these
• D. $\left(\frac{\alpha \beta r}{\alpha \beta }\right)$

Answer 1

The correct option is C None of these

Lets consider, $v=$ maximum velocity acquired by car

From 1st equation of motion,

$v=0+\alpha t_1$

$t_1=\frac{v}{\alpha }$

Similarly, $0=v-\beta t_2$

$t_2=\frac{v}{\beta }$

$t_1+t_2=t=\frac{v}{\alpha }+\frac{v}{\beta }$

$t=v\left(\frac{\alpha +\beta }{\alpha \beta }\right)$

$v=\frac{\alpha \beta }{\alpha +\beta }t$