A) 12 J
B) 9 J
C) 6 J
D) 3 J
Correct Answer: D
Solution :
\[s=\frac{{{t}^{2}}}{4}\] \\[ds=\frac{t}{2}dt\] \[F=ma=\frac{m{{d}^{2}}s}{d{{t}^{2}}}=\frac{6{{d}^{2}}}{d{{t}^{2}}}\left[ \frac{{{t}^{2}}}{4} \right]\ =\ 3N\] Now \[W=\int_{0}^{2}{F\,ds}=\int_{0}^{2}{3\frac{t}{2}dt}=\frac{3}{2}\left[ \frac{{{t}^{2}}}{2} \right]_{0}^{2}=\frac{3}{4}\left[ {{(2)}^{2}}-{{(0)}^{2}} \right]=3J\]
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