Work Energy And Power Question 257

Question: A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude pg. The instantaneous velocity of this car is proportiourl to:

Options:

A) $ {t^{2}}p _{o} $

B) $ {t^{1/2}} $

C) $ {t^{-1/2}} $

D) $ \frac{t}{\sqrt{m}} $

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Answer:

Correct Answer: B

Solution:

[b] Constant power of car $ P_0=F.V=ma.v $

$ P_0=m\frac{dv}{dt}.v $

$ P_0dt=mvdv $ Integrating $ P_0.t=\frac{mv^{2}}{2}v=\sqrt{\frac{2P_0t}{m}} $

$ \because ~~P_0, $ m and 2 are constant

$ \therefore v\propto \sqrt{t} $



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