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

Answer: 4. (2t³ + 3t⁵) W Key idea: power P=vec F·vec v ; find vec v by integrating vec a=vec F/m . vec a=2that i+3t²hat j (m = 1 kg), so vec v=t²hat i+t³hat j (starting from rest). P=(2t)(t²)+(3t²)(t³)=2t³+3t⁵ W.

Topic: Kinetic and potential energy, work-energy theorem· Work, Energy and Power

A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t^2 j) 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 ?

1. \((2t^2 + 3t^3)\) W

2. \((2t^2 + 4t^4)\) W

3. \((2t^3 + 3t^4)\) W

4. \((2t^3 + 3t^5)\) W

Doubtly Asked 30 Oct 2026 NEET UG 2016 Phase 1 Practice test neet Save WhatsApp Report

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Answer: 4. \((2t^3 + 3t^5)\) W

Key idea: power \(P=\vec F\cdot\vec v\); find \(\vec v\) by integrating \(\vec a=\vec F/m\).

\(\vec a=2t\hat i+3t^2\hat j\) (m = 1 kg), so \(\vec v=t^2\hat i+t^3\hat j\) (starting from rest).
\(P=(2t)(t^2)+(3t^2)(t^3)=2t^3+3t^5\) W.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t^2 j) 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 ?

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