A) \[\frac{m}{3P}(v_{2}^{3}-v_{1}^{3})\]
B) \[\frac{m}{3P}({{v}_{2}}-{{v}_{1}})\]
C) \[4.32\times {{10}^{6}}\]
D) \[\frac{m}{3P}(v_{2}^{2}-v_{1}^{2})\]
Correct Answer: A
Solution :
\[p=Fv=mav\] \[a=\frac{p}{mv}\] or \[v\frac{dv}{ds}=\frac{p}{mv}\] or \[{{v}^{2}}=dv=\frac{p}{m}ds\] or \[\frac{p}{m}\int_{0}^{s}{ds}=\int_{{{v}_{1}}}^{{{v}_{2}}}{{{v}^{2}}\,\,dv}\] or \[\frac{p}{m}s=\frac{1}{3}\,(v_{2}^{3}-v_{1}^{3})\] \[s=\frac{m}{3p}\,\,(v_{2}^{3}-v_{1}^{3})\]
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