A) 64 J
B) zero
C) - 64 J
D) None of these
Correct Answer: A
Solution :
Given, \[F=8t\] \[\Rightarrow \] \[m\frac{dv}{dt}=8t\] or \[m\int_{0}^{v}{dv=8}\,\int_{0}^{t}{t\,dt}\] \[\Rightarrow \] \[mv=4{{t}^{2}}\] or \[m\frac{dx}{dt}=4{{t}^{2}}\] \[\Rightarrow \] \[dx=\frac{4{{t}^{2}}}{m}dt=2{{t}^{2}}dt\] Now, \[W=\int{F\,dx=\int_{0}^{2}{(8t\times 2{{t}^{2}})}\,dt=64\,\,J}\]
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