Question

Power supplied to a particle of mass $2kg$ varies with time as $P=3t^2/2W$. Here t is in second. If the velocity of particle at $t=0$ is $v=0$, the velocity of particle at time $t=2s$ will be

• A. $1m{s}^{-1}$
• B. $4m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $2\sqrt{2}m{s}^{-1}$

Answer 1

Answer: (C)

$2m{s}^{-1}$

Power= $\frac{\text{Work done}}{Time}=\frac{dw}{dt}$

So, $dw=Pdt$

$P=\frac{3t^2}{2}$ (given)

So, $dw=\frac{3}{2}{t}^{2}dt$

now, $\underset{0}{\stackrel{w}{\int }}=\frac{3}{2}\underset{0}{\stackrel{2}{\int }}{t}^{2}dt$

So, $w=\frac{1}{2}[t^3{]}_0^2=4J$

Now, if the kinetic energy at time $t=2$ was $\frac{1}{2}m{v}^2$

where $v$ is the velocity at $t=2$

Then $\frac{1}{2}m{v}^2=4$

Given, $m=2kg$, or $v=2m/s$ .