A) 2 J
B) 3.8 J
C) 5.2 J
D) 24 J
Correct Answer: D
Solution :
\[S=\frac{{{t}^{3}}}{3}\]\ \[dS={{t}^{2}}dt\] \[a=\frac{{{d}^{2}}S}{d{{t}^{2}}}=\frac{{{d}^{2}}}{d{{t}^{2}}}\left[ \frac{{{t}^{3}}}{3} \right]=2t\ m/{{s}^{2}}\] Now work done by the force \[W=\int\limits_{0}^{2}{F.dS}=\int\limits_{0}^{2}{ma.dS}\] \[\int\limits_{0}^{2}{3\times 2t\times {{t}^{2}}dt}\]\[=\int\limits_{0}^{2}{6{{t}^{3}}dt}\]= \[\frac{3}{2}\left[ {{t}^{4}} \right]_{0}^{2}\]= 24 J
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