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. It total time elapsed is $t$, then maximum velocity acquired by car will be:

• A. $\frac{({\alpha }^2-{\beta }^2)t}{\alpha \beta }$
• B. $\frac{({\alpha }^2+{\beta }^2)t}{\alpha \beta }$
• C. $\frac{({\alpha }^{}+{\beta }^{})t}{\alpha \beta }$
• D. $\frac{\left({\alpha }^{}{\beta }^{}\right)t}{\alpha +\beta }$

Answer 1

The correct option is D $\frac{\left({\alpha }^{}{\beta }^{}\right)t}{\alpha +\beta }$

From rest, the car acceleraters for time t,

So $\alpha =\frac{V}{t_1}$ ...(1) , let maximum velocity is V.

The car begins decelerate after attaining maximum velocity

$\beta =\frac{V}{t-t_1}$ ....(2)

By adding 1 and 2

$t=v(\frac{1}{\alpha }+\frac{1}{\beta }$

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

Hence (D) is correct answer