Question

An object moving with an speed of 25 m/s is decelerating at a rate given by $a=-5\sqrt{v}$, where v is speed at any time. The time taken by the object to come to rest is:

• A. 1 s
• B. 5 s
• C. 2 s
• D. 3 s

Answer 1

The correct option is C 2 s

We know that acceleration is time derivative of velocity so the given relation can be written as $\frac{dv}{dt}=-5\sqrt[2]{2v}$ or $\frac{dv}{\sqrt[2]{2v}}=-5dt$integrating above equation we get $2\sqrt[2]{2v}=-5t+c$.....(1)

where c is integrating constant.

To evaluate the constant just put $t=0$ and $v=25$ as given in the question.

By doing so we lead to $c=10$ so the equation-1 becomes $2\sqrt[2]{2v}=-5t+10$ now put $v=0$ in above equation we get $t=2second$.

Option C is correct.