• # question_answer A force given by the relation $F=8t$ acts on a body of mass 2 kg initially at rest. Find the work done by this force on the body during first 2 s of its motion. A)  64 J                            B)  zero              C)  - 64 J                          D)  None of these

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, $W=\int{F\,dx=\int_{0}^{2}{(8t\times 2{{t}^{2}})}\,dt=64\,\,J}$