A) \[\frac{m}{3P}(v_{2}^{3}-v_{1}^{3})\]
B) \[\frac{m}{3P}({{v}_{2}}-{{v}_{1}})\]
C) \[\frac{3p}{m}(v_{2}^{2}-v_{1}^{2})\]
D) \[\frac{m}{3P}(v_{2}^{2}-v_{1}^{2})\]
Correct Answer: A
Solution :
| [a] \[P=Fv=mav\] |
| \[\Rightarrow \] \[a=\frac{P}{mv}\] |
| \[\Rightarrow \] \[v\frac{dv}{ds}=\frac{P}{mv}\] |
| \[\Rightarrow \] \[{{v}^{2}}dv=\frac{P}{m}ds\] |
| \[\Rightarrow \] \[\frac{P}{m}\int_{\,0}^{\,s}{ds}=\int_{\,{{v}_{1}}}^{\,{{v}_{2}}}{{{v}^{2}}dv}\] |
| \[\Rightarrow \] \[\frac{P}{m}s=\frac{1}{3}(v_{2}^{3}-v_{1}^{3})\] |
| \[\Rightarrow \] \[s=\frac{m}{3P}(v_{2}^{3}-v_{1}^{3})\] |
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