A) 64 J
B) 128 J
C) 200 J
D) 240 J
Correct Answer: B
Solution :
Velocity of body at time t is given by \[v=\frac{dx}{dt}=\frac{d}{dt}({{t}^{2}})=2t\] Now, at \[\operatorname{t} = 0 s\], initial velocity \[{{\operatorname{v}}_{i}} = 0\] at \[\operatorname{t} = 4\,s\], final velocity \[{{v}_{f}} = 8\] \[\operatorname{Work} done = Increase in KE\] \[=\frac{1}{2}mv_{f}^{2}-\frac{1}{2}mv_{i}^{2}\] \[=\,\,\,\,\frac{1}{2}m\,(v_{f}^{2}-v_{i}^{2})\] \[=\,\,\,\frac{1}{2}\times 4\times ({{8}^{2}}-{{0}^{2}})=128\,\,J\]
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