Question

An object moving with a speed of 6.25 m/s, is decelerated at a rate given by:

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

where v is instantaneous speed. The time taken by the object, to come to rest, would be:

• A. 1 s
• B. 2 s
• C. 4 s
• D. 8 s

Answer 1

The correct option is B 2 s

Given,

Speed of the object = 6.25 m/s

The final speed of the object = 0

Relation given as

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

We can write it as

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

Integrating both sides

${\int }_{6.25}^0\frac{dv}{\sqrt{v}}=-2.5{\int }_0^{t}dt$

After solving

$2\sqrt{6.25}=2.5t$

Or, t = 2 s

Hence, the time taken by the object to come to rest is 2 seconds