A body of mass 1 kg begins to move under the action of a time dependent force F = (ti + 2t²j) N, where i and j are unit vectors along x and y axis. The power developed by above force at time t = 3 second will be (a) 337.5 W (b) 228.5 W (c) 422.5 W (d) 126.5 W

Answer: (a). m = 1 kg, so a = ti + 2t²j; from rest v = t²/2i + 2t³/3j. At t = 3: F = 3i + 18j, v = 4.5i + 18j. P = F · v = 13.5 + 324 = 337.5 W So the answer is (a) 337.5 W.

A body of mass 1 kg begins to move under the action of a time… | MHT CET 2025 (22 Apr, Shift 1)

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Power

A body of mass 1 kg begins to move under the action of a time dependent force $\vec{F} = \left(t\hat{i} + 2t^2\hat{j}\right)\text{ N}$ , where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axis. The power developed by above force at time $t = 3$ second will be

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Answer: (a)

$m = 1$ kg, so $\vec{a} = t\hat{i} + 2t^2\hat{j}$ ; from rest $\vec{v} = \dfrac{t^2}{2}\hat{i} + \dfrac{2t^3}{3}\hat{j}$ .
At $t = 3$ : $\vec{F} = 3\hat{i} + 18\hat{j}$ , $\vec{v} = 4.5\hat{i} + 18\hat{j}$ .
$P = \vec{F} \cdot \vec{v} = 13.5 + 324 = 337.5\text{ W}$
So the answer is (a) 337.5 W.

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