A body of mass 1 kg begins to move under the action of a time dependent force F = (2ti + 3t²j)N, where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t? (a) (2t3 + 3t4) W (b) (2t3 + 3t5) W (c) (2t2 + 3t3) W (d) (2t2 + 4t4) W

Answer: (b). m = 1 kg, so a = 2ti + 3t²j; from rest v = t²i + t³j. P = F · v = (2t)(t²) + (3t²)(t³) = 2t³ + 3t⁵ So the answer is (b) (2t³ + 3t⁵) W.

A body of mass 1 kg begins to move under the action of a time… | NEET 2016 (Phase 1)

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Power

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

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Answer: (b)

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

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