An object of mass 1000 g experiences a time dependent force F = (2ti + 3t²j)N. The power generated by the force at time t is: (a) (2t² + 18t³)W (b) (3t³ + 5t⁵)W (c) (2t³ + 3t⁵)W (d) (2t² + 3t³)W

Answer: (c). m = 1 kg, so a = 2ti + 3t²j; from rest v = t²i + t³j. P = F · v = 2t³ + 3t⁵ So the answer is (c) (2t³ + 3t⁵) W.

An object of mass 1000 g experiences a time dependent force F = (2ti… | JEE Main 2025 (7 Apr, Shift 1)

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Power

An object of mass 1000 g experiences a time dependent force $\vec{F} = \left(2t\hat{i} + 3t^2\hat{j}\right)N$ . The power generated by the force at time $t$ is:

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Answer: (c)

$m = 1$ kg, so $\vec{a} = 2t\hat{i} + 3t^2\hat{j}$ ; from rest $\vec{v} = t^2\hat{i} + t^3\hat{j}$ .
$P = \vec{F} \cdot \vec{v} = 2t^3 + 3t^5$
So the answer is (c) $(2t^3 + 3t^5)$ W.

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