First slide

Power

Question

Power supplied to a particle of mass 2 kg varies with time as $P = \frac{3 t^{2}}{2} W$ . Hence, t second. If particIe is
rest at t = 0, then velocity of particle at time t = 2s will be

Moderate

A

1 $m s^{- 1}$
B

4 $m s^{- 1}$
C

2 $m s^{- 1}$
D

2 $\sqrt{2}$ $m s^{- 1}$

Solution

Work done, $W = \int P d t or \frac{1}{2} m v^{2} = \int P d t = \int_{0}^{2} (\frac{3 t^{2}}{2}) d t = 4]$
$\Rightarrow v = \sqrt{\frac{8}{2}} = 2 {ms}^{- 1}$

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