Question

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

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

Answer 1

Answer: (C)

$2\,ms^{-1}$

Answer 2

From work energy theorem, $\Delta KE=W_{\text{net}}$ $K_{fi}-K_{i}=\int{P}\,\,dt$ $\frac{1}{2}m{{v}^{2}}-0=\int\limits_{0}^{2}{\left( \frac{3}{2}{{t}^{2}} \right)dt}$ $\frac{1}{2}(2){{v}^{2}}=\frac{3}{2}\left[ \frac{{{t}^{3}}}{3} \right]_{0}^{2}=4$ $v = 2\,ms^{-1}$