An object moving along horizontal x-direction with kinetic energy \(10 \, \text{J}\) is displaced through \(\mathbf{x} = (3\mathbf{i}) \, \text{m}\) by the force \(\mathbf{F} = (-2\mathbf{i} + 3\mathbf{j}) \, \text{N}\). The kinetic energy of the object at the end of the displacement \(\mathbf{x}\) is:
- \(10 \, \text{J}\)
- \(16 \, \text{J}\)
- \(4 \, \text{J}\)
- \(6 \, \text{J}\)
The Correct Option is C
Solution and Explanation
Work done (W) = $\vec{F} \times \vec{x} = (-2\hat{i} + 3\hat{j}) \times (3\hat{i}) = -6 \text{ J}$.
Work-energy theorem: W = ΔKE = KEf - KEi = -6 J = KEf - 10 J KEf = 4 J
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