Work Energy Theorem

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Question

A force of $\vec{F} = (2 \hat{i} + 3 \hat{j})$ acting on a body mass 2kg which was initially at rest. If the displacement produced by the force is 12 $\hat{i}$ +8 $\hat{j}$ .Then the final velocity of the body is

Moderate

Solution

work done $\vec{F} . \vec{S} = \frac{1}{2} m v^{2} - 0$ = change in kinetic energy
$(2 \hat{i} + 3 \hat{j}) . (12 \hat{i} + 8 \hat{j}) = 48 J$
$\frac{1}{2} m v^{2} = 48$ , v= $4 \sqrt{3}$

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