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JEE Main 2021 (27 Jul, Shift 2) · Power

Power question from JEE Main 2021 (27 Jul, Shift 2)

Q29JEE Main 2021 · 27 JUL · SHIFT 2Medium

Power

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

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Answer: (d)

  1. Pt=12mv2⇒v=2Pm t1/2Pt = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{\frac{2P}{m}}\,t^{1/2}
  2. x=∫0tv dt=2Pm⋅23t3/2x = \int_0^t v\,dt = \sqrt{\frac{2P}{m}} \cdot \frac{2}{3}t^{3/2}
  3. x=(8P9m)1/2t3/2x = \left(\frac{8P}{9m}\right)^{1/2} t^{3/2}
  4. So the answer is (d).
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