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)

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 $