Question

Power supplied to a particle of mass $2Kg$ varies with time as $p=3t^2/2$ watt. Here $t$ is in seconds. If velocity of particle at $t=0$ is $v=0$, the velocity of particle at time $t=2s$ will be:

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

Answer 1

The correct option is C $2m/s$

Solution

We have,

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

As, $P=\frac{dw}{dt}$

$\Rightarrow △W={\int }_0^{t}p.dt={\int }_0^t\left(\frac{3t^2}{2}\right).dt$

$△W=[\frac{t^3}{2}{]}_0^t$

$\Rightarrow △W=\left(t^3\right)/2$

We know by work - Energy theorem

$△W=△KE=\frac{M}{2}\left[V\right(t{)}^2-V\left(0{)}^2\right]$

$△W=\frac{MV(t{)}^2}{2}$

$\Rightarrow \frac{\left(t^3\right)}{2}=\frac{MV(t{)}^2}{2}$

At $t=2s$,

$(2{)}^3=(2)V^2\Rightarrow V=2m/s$

Option - C is correct.