A) \[{{t}^{1/2}}\]
B) \[{{t}^{3/4}}\]
C) \[t\]
D) \[{{t}^{3/2}}\]
E) \[{{t}^{2}}\]
Correct Answer: D
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\[{{t}^{3/2}}\].
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