Question

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

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

Answer 1

The correct option is B $2s$

$\frac{dv}{dt}=-2.5\sqrt{v}\int \frac{dv}{\sqrt{v}}=\int -2.5dt{\left[2\sqrt{v}\right]}_{6.25}^0=-2.5{\left[t\right]}_0^t-2\times 2.5=-2.5tt=2sec$