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(C) Power $P$ is given by $P = Fv = mav = m(dv/dt)v$.Rearranging the terms,we get $(P/m) dt = v dv$.Integrating both sides,$\int (P/m) dt = \int v dv$

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$t^{3/2}$

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(C) Power $P$ is given by $P = Fv = mav = m(dv/dt)v$.Rearranging the terms,we get $(P/m) dt = v dv$.Integrating both sides,$\int (P/m) dt = \int v dv$,which gives $(P/m)t = v^2/2$.Thus,$v = (2P/m)^{1/2} t^{1/2}$.Since $v = ds/dt$,we have $ds = (2P/m)^{1/2} t^{1/2} dt$.Integrating $s = \int ds = (2P/m)^{1/2} \int t^{1/2} dt = (2P/m)^{1/2} [t^{3/2} / (3/2)]$.Therefore,$s = (2/3)(2P/m)^{1/2} t^{3/2}$,which implies $s \propto t^{3/2}$.

$A$ body is moving in 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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