Question

A car moving with a velocity $6.25\, ms ^{-1}$ is decelerated with $2.5 \,\sqrt{ v } ms ^{-2}(v$ 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, $u=6.25\, ms ^{-1}$ and $a=-2.5 \sqrt{v} \,ms ^{-2}$,
$v=$ instantaneous velocity
As we know,
$a=\frac{d v}{d t} $
So, $\frac{d v}{d t}=-2.5 \sqrt{v}$
Integrate on the both sides, we get
$\Rightarrow \, \int\limits_{6.25}^{0} \frac{1}{\sqrt{v}} d v=-2.5 \int d t $
$\Rightarrow \, {[2 \sqrt{v}]_{6.25}^{0}=-2.5 t} $
$\Rightarrow \, t=\frac{2 \times 2.5}{2.5}=2\, s$