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A body of mass 1 kg begins to move under the action of a time dependent force F̅ = (2tî + 3t²ĵ) N, where î and ĵ are unit vectors along x and y-axis. What power will be developed by the force at time t?

1. (2t² + 3t³)W
2. (2t² + 4t³)W
3. (2t³ + 3t⁴)W
4. (2t³ + 3t⁵)W

Correct answer: (2t² + 3t³)W

Solution

The power developed by the force is given by P = F̅ · v̅, where v̅ is the velocity of the body. The velocity is obtained by integrating the acceleration (F̅/m) with respect to time. After integration, v̅ = (t²î + t³ĵ) m/s. Substituting F̅ and v̅ into the power formula, P = (2tî + 3t²ĵ) · (t²î + t³ĵ) = 2t³ + 3t⁴ W.

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