A) \[{{t}^{1/2}}\]
B) \[{{t}^{3/4}}\]
C) \[{{t}^{3/2}}\]
D) \[{{t}^{2}}\]
Correct Answer: C
Solution :
\[\text{P}=\text{Fv}=mav=m\left( \frac{dv}{dt} \right)\text{ }v\text{ }\Rightarrow \frac{P}{m}\text{dt}=v\text{ }dv\] Now \[\Rightarrow \,\,\,\frac{P}{m}\,\times \,t=\frac{{{v}^{2}}}{2}\,\,\Rightarrow \,\,v={{\left( \frac{2P}{m} \right)}^{1/2}}\,\,({{t}^{1/2}})\] \[\therefore \,\,s={{\left( \frac{2P}{m} \right)}^{1/2}}\,\,\left[ \frac{2{{t}^{3/2}}}{3} \right]\,\,\,\Rightarrow \,\,s\propto \,\,{{t}^{3/2}}\]
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