Question

A car moving with a velocity $6.25m{s}^{-1}$ is decelerated with $2.5\sqrt{v}m{s}^{-2}(v$ is instantaneous velocity). Time taken by the car to come to rest is

• A. 2 s
• B. 3 s
• C. 2.5 s
• D. 4 s

Answer 1

Answer: (A)

Given, $u=6.25m{s}^{-1}$ and $a=-2.5\sqrt{v}m{s}^{-2}$,
$v=$ instantaneous velocity
As we know,
$a=\frac{dv}{dt}$
So, $\frac{dv}{dt}=-2.5\sqrt{v}$
Integrate on the both sides, we get
$\Rightarrow \underset{6.25}{\overset{0}{\int }}\frac{1}{\sqrt{v}}dv=-2.5\int dt$
$\Rightarrow [2\sqrt{v}{]}_{6.25}^0=-2.5t$
$\Rightarrow t=\frac{2\times 2.5}{2.5}=2s$