Question

Velocity of a particle is given as $V=4-t^2$. If the particle starts its motion from origin then, time after which it will be again at origin is

• A. $4sec$
• B. $\sqrt{12}sec$
• C. $3sec$
• D. $\sqrt{15}sec$

Answer 1

The correct option is B $\sqrt{12}sec$

$V=4-t^2\Rightarrow \frac{dx}{dt}=4-t^2$
${\int }_0^{0}dx={\int }_0^t(4-t^2)dt\Rightarrow 0=4t-\frac{t^3}{3}$
$(4-\frac{t^2}{3})t=0\Rightarrow t^2=12\Rightarrow t=\sqrt{12}$