First slide

Power

Question

A particle of mass 0.5 kg is moving in xy plane with acceleration $\vec{a} = (3 \hat{i} + 2 t \hat{j}) m / s^{2} .$ At time t, its velocity is given by $\vec{V} = (2 t \hat{i} + 3 t^{2} \hat{j}) m / s .$ Then rate of work done on the particle at t = 1 sec is

Easy

A

6 watt
B

8 watt
C

12 watt
D

24 watt

Solution

(1)
Force acting on the particle,
$\begin{array}{l} \vec{F} = m \vec{a} = 0.5 (3 \hat{i} + 2 t \hat{j}) N \\ ∴ P o w e r, P = \vec{F} . \vec{V} = 0.5 (3 \hat{i} + 2 t \hat{j}) . (2 t \hat{i} + 3 t \hat{j}) \\ = \frac{1}{2} (6 t + 6 t^{3}) w a t t \\ P = 3 (t + t^{3}) w a t t \\ A t t = 1 \sec, P = 3 (1 + 1) w a t t = 6 w a t t . \end{array}$

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