First slide

Power

Question

Power supplied to a particle of mass 2 kg varies with time as $P = \frac{3 t^{2}}{2}$ watt, 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

Moderate

A

1 ms^-1
B

4 ms^-1
C

2 ms^-1
D

$2 \sqrt{2}$ ms^-1

Solution

From work-energy theorem,
$\begin{array}{l} ΔKE = W_{net} \\ K_{f} - K_{i} = \int Pdt \\ \frac{1}{2} {mv}^{2} = \int_{0}^{2} (\frac{3}{2} t^{2}) dt \\ v^{2} = {[\frac{t^{3}}{2}]}_{0}^{2} \\ v = 2 {ms}^{- 1} \end{array}$

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