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  4. A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

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Q. A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

KEAMKEAM 2000

Solution:

Power $ (P)=[M{{L}^{2}}{{T}^{-3}}] $ $ \therefore $ $ [{{L}^{2}}]=\frac{P}{[M{{T}^{-3}}]}=[P{{M}^{-1}}{{T}^{3}}] $ As P and M are constant, therefore $ {{L}^{2}}\propto {{T}^{3}} $ $ \Rightarrow $ $ L\propto {{T}^{3/2}} $ $ \Rightarrow $ The distance moved by the body in time t is proportional to $ {{t}^{3/2}} $ .