A body of mass 2 kg begins to move under the action of a time dependent force given by F = (6ti + 6t²j)N. The power developed by the force at the time t is given by: (a) (3t³ + 6t⁵)W (b) (9t⁵ + 6t³)W (c) (6t⁴ + 9t⁵)W (d) (9t³ + 6t⁵)W

Answer: (d). a = F/2 = 3ti + 3t²j; from rest v = 3t²/2i + t³j. P = F · v = (6t)(3t²/2) + (6t²)(t³) = 9t³ + 6t⁵ So the answer is (d) (9t³ + 6t⁵) W.

A body of mass 2 kg begins to move under the action of a time… | JEE Main 2024 (31 Jan, Shift 2)

Q15JEE Main 2024 · 31 JAN · SHIFT 2Medium

Power

A body of mass $2\text{ kg}$ begins to move under the action of a time dependent force given by $\vec{F} = \left(6t\hat{i} + 6t^2\hat{j}\right)N$ . The power developed by the force at the time $t$ is given by:

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Answer: (d)

$\vec{a} = \dfrac{\vec{F}}{2} = 3t\hat{i} + 3t^2\hat{j}$ ; from rest $\vec{v} = \dfrac{3t^2}{2}\hat{i} + t^3\hat{j}$ .
$P = \vec{F} \cdot \vec{v} = (6t)\left(\dfrac{3t^2}{2}\right) + (6t^2)(t^3) = 9t^3 + 6t^5$
So the answer is (d) $(9t^3 + 6t^5)$ W.

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