Question

Power supplied to a particle of mass 2 kg varies with time as $P=\frac{3{{t}^{2}}}{2}W.$ 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 m/s
• B. 4 m/s
• C. 2 m/s
• D. $2\sqrt{2}\,m/s$

Answer 1

Answer: (C)

2 m/s

Answer 2

From work energy theorem
$\Delta KE =W{{E}_{net}}$
or ${{K}_{f}}-{{K}_{i}}=\int_{{}}^{{}}{p\,dt}$
$\frac{1}{2}m{{v}^{2}}-0=\int_{0}^{2}{\left( \frac{3}{2}{{t}^{2}} \right)}\,dt$
${{v}^{2}}=\left[ \frac{{{t}^{3}}}{2} \right]_{0}^{2}$
$v=2m/s$