Question

A body of mass $$6\,kg$$  is under a force which causes displacement in it given by $$S = \dfrac{{{t^2}}}{4}$$  metres where $$t$$ is time. The work done by the force in $$2$$ seconds is:-

A
12J
B
9J
C
6J
D
3J

Solution

The correct option is D $$3\,J$$we havedisplacement ($$s$$) given as$$s=\cfrac{{t}^{2}}{4}$$so, velocity $$v=\cfrac{ds}{dt}$$i.e $$v=\cfrac{2t}{v}$$$$v=\cfrac{t}{2}{ms}^{-1}$$Now at $$t=0$$. velocity $${v}_{1}=0$$and hence kinetic energy $${k}_{1}=0$$at $$t=2sec$$velocity $${v}_{2}=\cfrac{2}{2}=1{ms}^{-1}$$So, kinetic energy, $${k}_{2}=\cfrac{1}{2}m{v}_{2}^{2}=\cfrac{1}{2}\times 6\times {(1)}^{2}$$$$=3J$$By work energy theoremWork done by the force $$=$$ change in kinetic energyi.e., $$w=\Delta K$$$$w={K}_{2}-{K}_{1}=3-0$$Work done $$($$w$$)=3$$ joulePhysics

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