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

• A. 2 s
• B. 4 s
• C. 8 s
• D. 1 s

Answer 1

The correct option is A 2 s

$Accordingtoquestion...................{\int }_{6.25}^0\left(\frac{dv}{\sqrt{v}}\right)=-2.5{\int }_0^{t}dt\Rightarrow {\left|2\sqrt{v}\right|}_{6.25}^0=-2.5t\Rightarrow 2.\sqrt{6.25}=2.5t\therefore t=2ssothecorrectoptuonisA$