A) \[\frac{1}{2}\left[ \frac{m{{v}^{2}}}{t_{1}^{2}} \right]{{t}^{2}}\]
B) \[\frac{1}{2}\left[ \frac{mv}{{{t}_{1}}} \right]{{t}^{2}}\]
C) \[\left[ \frac{m{{v}^{2}}}{t_{1}^{2}} \right]{{t}^{2}}\]
D) \[\left[ \frac{2\,m{{v}^{2}}}{t_{1}^{2}} \right]{{t}^{2}}\]
Correct Answer: A
Solution :
[a] \[v-u=at\] \[v-0=a{{t}_{1}}(u=0\,starts\,from\,\,rest)\] \[a=\frac{v}{{{t}_{1}}}.....(1)\] \[S=ut+\frac{1}{2}a{{t}^{2}}\] \[S=\frac{1}{2}a{{t}^{2}}(u=0)\] \[S=\frac{1}{2}\frac{v}{{{t}_{1}}}{{t}^{2}}\] \[W=F.S\] \[=m\,a\,s\] \[=\frac{mv}{{{t}_{1}}}.\frac{1}{2}\frac{v}{{{t}_{1}}}{{t}^{2}}\] \[=\frac{1}{2}=\frac{m{{v}^{2}}{{t}^{2}}}{t_{1}^{2}}\]
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