First slide

Power

Question

A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N$ where $\hat{i} and \hat{j}$ jare unit vectors along x and y-axis. What power will be developed by the force at the time t

Easy

A

(2t² +3t³)w
B

(2t² +4t²)w
C

(2t³ +3t³)w
D

(2t³ +3t⁵)w

Solution

$\vec{F} = 2 t \hat{i} + 3 t^{2} \hat{j} \Rightarrow m \frac{d \vec{v}}{dt} = 2 t \hat{i} + 3 t^{2} \hat{j} {m = 1 kg}$
$\begin{array}{l} \Rightarrow \int_{0}^{v} d \vec{v} = \int_{0}^{t} (2 \hat{i} + 3 t^{2} \hat{j}) dt \Rightarrow \vec{v} = t^{2} \hat{i} + t^{3} \hat{j} \\ Power = \vec{F} \cdot \vec{v} = (2 t^{3} + 3 t^{5}) W \end{array}$

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