Work Energy And Power Question 72

Question: A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to [IIT 1984; BHU 1984, 95; MP PET 1996; JIPMER 2000; AMU (Med.) 1999]

Options:

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

B) $ {t^{3/4}} $

C) $ {t^{3/2}} $

D) $ t^{2} $

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Answer:

Correct Answer: C

Solution:

$ P=Fv=mav=m( \frac{dv}{dt} )\ v $

therefore $ \frac{P}{m}dt=v\ dv $

therefore $ \frac{P}{m}\times t=\frac{v^{2}}{2} $

therefore $ v={{( \frac{2P}{m} )}^{1/2}}{{(t)}^{1/2}} $ Now $ s=\int _{{}}^{{}}{v\ dt=\int _{{}}^{{}}{{{( \frac{2P}{m} )}^{1/2}}{t^{1/2}}dt}} $ \ $ s={{( \frac{2P}{m} )}^{1/2}}[ \frac{2{t^{3/2}}}{3} ] $

therefore $ s\propto {t^{3/2}} $



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