Question

Power supplied to a particle of mass $2\text{kg}$ varies with time as $P=\frac{3t^2}{2}$ watt. Here $t$ is in second. If velocity of particle at $t=0$ is $v=0$. The velocity of particle at time $t=2$ s will be

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

Answer 1

The correct option is C $2\text{m/s}$

$W=\int Pdt\frac{1}{2}m{v}^2=\int Pdt={\int }_0^2\left(\frac{3t^2}{2}\right)dt=4J$
$\therefore v=\sqrt{\frac{2\times 4}{2}}=2\text{m/s}$