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An object, moving with a speed of $6.25 m/s$, is decelerated at a rate given by: $dv/dt = -2.5\sqrt{v}$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be
Explanation
$dv/dt = -2.5\sqrt{v} \Rightarrow dv/\sqrt{v} = -2.5dt$ Integrating, $\int_{6.25}^{0}{v^{- 1/2}dv = 2.5\int_{0}^{t}{dt = \left[ \frac{v^{+ 1/2}}{\frac{1}{2}} \right]_{6.25}^{0} = - 2.5{[ t]}_{0}^{t}}}$ $\Rightarrow - 2(6.25)1/2 = - 2.5t \Rightarrow t = 2sec$