A body of mass 2 kg begins to move under the influence of time dependent force F = (2ti + 6t²j) N, where i and j are unit vectors along x and y -axis respectively. The power produced by the force at t = 2 s is ______ W. Numerical answer type. Work it out, then open the answer.

Answer: 200. a = F/2 = ti + 3t²j; from rest v = t²/2i + t³j. At t = 2: F = 4i + 24j, v = 2i + 8j. P = F · v = 8 + 192 = 200 W

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Power

A body of mass 2 kg begins to move under the influence of time dependent force $\vec{F} = \left(2t\hat{i} + 6t^2\hat{j}\right)\text{ N}$ , where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and y -axis respectively. The power produced by the force at $t = 2\text{ s}$ is ______ W.

Numerical answer type. Work it out, then open the answer.

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Answer: 200

$\vec{a} = \dfrac{\vec{F}}{2} = t\hat{i} + 3t^2\hat{j}$ ; from rest $\vec{v} = \dfrac{t^2}{2}\hat{i} + t^3\hat{j}$ .
At $t = 2$ : $\vec{F} = 4\hat{i} + 24\hat{j}$ , $\vec{v} = 2\hat{i} + 8\hat{j}$ .
$P = \vec{F} \cdot \vec{v} = 8 + 192 = 200\text{ W}$

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