A body of mass 1kg begins to move under the action of a time dependent force F = (ti + 3t²j) N where i and j are the unit vectors along x and y axis. The power developed by the above force at time t = 2 s will be (in watt) (a) 100 (b) 50 (c) 25 (d) 5

Answer: (a). m = 1 kg, so a = ti + 3t²j; from rest v = t²/2i + t³j. At t = 2: F = 2i + 12j, v = 2i + 8j. P = F · v = 4 + 96 = 100 W So the answer is (a) 100.

A body of mass 1kg begins to move under the action of a time… | MHT CET 2026 (16 Apr, Shift 2)

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Power

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

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Answer: (a)

$m = 1$ kg, so $\vec{a} = t\hat{i} + 3t^2\hat{j}$ ; from rest $\vec{v} = \dfrac{t^2}{2}\hat{i} + t^3\hat{j}$ .
At $t = 2$ : $\vec{F} = 2\hat{i} + 12\hat{j}$ , $\vec{v} = 2\hat{i} + 8\hat{j}$ .
$P = \vec{F} \cdot \vec{v} = 4 + 96 = 100\text{ W}$
So the answer is (a) 100.

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