Power supplied to a particle of mass 2 kg varies with time as \(P = \frac{3t^2}{2}\) W. Here t is in second. If the velocity of particle at t = 0 is v = 0, the velocity of particle at time t = 2 s will be :
Answer & explanation
Correct answer: option 4
From Work-Energy Theorem :
\(W_{net} = \Delta KE = K_f - K_i\)
\(W_{net} = \int P dt\)
\(\Rightarrow \frac{1}{2}mv^2 - 0 = \int_0^2 (\frac{3}{2}t^2)dt\)
\(\Rightarrow v^2 = |\frac{t^3}{2}|^2_0\)
\(\Rightarrow v = 2 \text{ m/s}\)