A) \[{{t}^{\frac{1}{2}}}\]
B) \[{{t}^{\frac{3}{4}}}\]
C) \[{{t}^{\frac{3}{2}}}\]
D) \[{{t}^{2}}\]
Correct Answer: C
Solution :
\[P=Fv=mav=m\left( \frac{dv}{dt} \right)v=\frac{P}{m}dt=vdv\] \[\Rightarrow \]\[\frac{P}{m}\times t=\frac{{{v}^{2}}}{2}\Rightarrow v={{\left( \frac{2P}{m} \right)}^{1/2}}{{t}^{1/2}}\] Now, \[s=\int_{{}}^{{}}{vdt}={{\int_{{}}^{{}}{\left( \frac{2P}{m} \right)}}^{1/2}}{{t}^{1/2}}dt\] \[\therefore \] \[s={{\left( \frac{2P}{m} \right)}^{1/2}}{{t}^{1/2}}dt\] Hence, the correction option is [c].
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