A) \[{{t}^{2}}{{P}_{0}}\]
B) \[{{t}^{1/2}}\]
C) \[{{t}^{-1/2}}\]
D) \[t/\sqrt{m}\]
Correct Answer: B
Solution :
Power \[{{p}_{0}}=Fv=\left( m\frac{dv}{dt} \right)v=mv\frac{dv}{dt}\] Integrating both sides \[\int_{{}}^{{}}{{{p}_{0}}dt=\int_{{}}^{{}}{mv\,dv}\Rightarrow \,{{p}_{0}}t=\frac{m{{v}^{2}}}{2}}\] \[{{v}^{2}}=\frac{2{{p}_{0}}t}{m}\Rightarrow v\propto {{t}^{1/2}}\]
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