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