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  4. An object, moving with a speed of 6.25 m / s, is decelerated at a rate given by (d v/d t)=-2.5 √v where v is the instantaneous speed. The time taken by the object, to come to rest, would be

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Q. An object, moving with a speed of $6.25 m / s$, is decelerated at a rate given by
$\frac{d v}{d t}=-2.5 \sqrt{v}$
where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be

AIEEEAIEEE 2011

Solution:

$\int\limits_{v}^{0} \frac{d v}{\sqrt{v}}=-\int\limits_{0}^{t} 2.5 d t$
$2 \sqrt{v}=2.5 t$
$2 \sqrt{6.25}=2.5 t$
$t=2 s$