First slide

Work

Question

A force $\vec{F} = (2 t i + 5 t^{2} \hat{j}) N$ acts on a body due to which displacement varies as $\vec{S} = (3 t^{2} \hat{i} + 4 \hat{k}) m$ work done in 3 seconds is

Moderate

A

142J
B

322J
C

108J
D

38J

Solution

$\begin{array}{l} \vec{S} = 3 t^{2} \hat{i} + 4 \hat{k} \\ \Rightarrow \vec{ds} = 6 tdt \hat{i} \\ W = \int \bar{F} \cdot \vec{ds} = \int (2 \hat{t} + 5 t^{2} \hat{j}) \cdot (6 tdt \hat{i}) \\ W = 12 \int_{0}^{3} t^{2} dt = 12 \times {[\frac{t^{3}}{3}]}_{0}^{3} = 4 \times 27 \\ W = 108 J \end{array}$

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