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

The Correct Option is C

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 $ $v = 2\,ms^{-1}$