Question

An object, moving with a speed of $6.25m{s}^{-1}$, is decelerated at a rate given by $\frac{dv}{dt}=-2.5\sqrt{v}$ where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be

• A. $1s$
• B. $2s$
• C. $4s$
• D. $8s$

Answer 1

The correct option is B $2s$

${\int }_{6.25}^0\frac{dv}{\sqrt{v}}=-2.5{\int }_0^{t}dt$
By calculating this we get,
$\therefore t=2s$