A) s
B) \[\sqrt{2}\,s\]
C) \[{{s}^{2}}\]
D) None of these
Correct Answer: B
Solution :
As, \[\operatorname{a} = 2s\] \[\Rightarrow \,\,\,\,\frac{dv}{dt}=2s\] \[\Rightarrow \,\,\,\,\frac{dv}{ds}\,\frac{ds}{dt}=2s\] \[\Rightarrow \,\,\,\,\frac{dv}{ds}\,v=2s\] \[\Rightarrow \,\,\,\,v\,\,dv=2s\,\,ds\] \[\Rightarrow \,\,\,\,\int_{0}^{v}{vdv}\,\,=\,\,\int_{0}^{s}{2s\,\,ds}\,\] \[\Rightarrow \,\,\,\,\left[ \frac{{{v}^{2}}}{2} \right]_{0}^{v}\,\,\,=\,\,2\left[ \frac{{{s}^{2}}}{2} \right]_{0}^{s}\] \[\Rightarrow \,\,\,\,\frac{{{v}^{2}}}{2}={{s}^{2}}\,\,\,\Rightarrow \,\,\,v=\sqrt{2}\,s\]
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