An object moving with a speed of 6.25 m/s, is decelerated at a rage given by dv/dt =-2.5√v , where v is instantaneous speed.

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

Sol:$\large \frac{dv}{dt} = -2.5 \sqrt{v} $

$\large \frac{dv}{\sqrt{v} } = -2.5 dt $

$\large \int_{6.25}^{0}\frac{dv}{\sqrt{v}} = -2.5 \int_{0}^{t} dt $

$\large 2[v^{1/2}]_{6.25}^{0} = -2.5 t $

t = 2 sec