An object moving along horizontal x -direction with kinetic energy 10 J is displaced through x = (3i) m by the force F = (-2i + 3j) N. The kinetic energy of the object at the end of the displacement x is (a) 10 J (b) 16 J (c) 4 J (d) 6 J

Answer: (c). W = F = (-2)(3) + 3(0) = -6 J Work-energy theorem: Kf = Ki + W = 10 - 6 = 4 J So the answer is (c) 4 J.

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Work by a Variable Force

An object moving along horizontal $x$ -direction with kinetic energy $10\text{ J}$ is displaced through $x = (3\hat{i})\text{ m}$ by the force $\vec{F} = (-2\hat{i} + 3\hat{j})\text{ N}$ . The kinetic energy of the object at the end of the displacement $x$ is

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Answer: (c)

$W = \vec{F}\cdot\vec{s} = (-2)(3) + 3(0) = -6$ J
Work-energy theorem: $K_f = K_i + W = 10 - 6 = 4$ J
So the answer is (c) $4\text{ J}$ .

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