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  4. 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:

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Q. 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:

JIPMERJIPMER 2000

Solution:

As power $ =F\times \upsilon =m\frac{dv}{dt}\times v= $ constant k $ \upsilon d\upsilon =\frac{k}{m}dt $ ?(i) Now integrating equation (i), we get $ {{\upsilon }^{2}}=\frac{2kt}{m} $ or $ \upsilon =\frac{dx}{dt}=\sqrt{\frac{2k}{m}}{{t}^{1/2}} $ hence $ x\propto {{t}^{3/2}} $