Question

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

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

Answer 1

The correct option is A $2s$

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

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

${\int }_{6.25}^0{v}^{-1/2}dv=-2.5{\int }_0^{t}dt$

$-2.5[t{]}_0^t=[2v^{1/2}{]}_{6.25}^0$

$t=2s$

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

${\int }_{6.25}^0{V}^{-1/2}dv=-2.5{\int }_0^{t}dt$

$-2.5[t{]}_0^t=[2v^{1/2}{]}_{6.25}^0$

$t=2seconds$

Hence (A) option is corrcet