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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
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B
9J
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C
6J
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D
3J
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Solution

The correct option is D $$3\,J$$
we have
displacement ($$s$$) 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 theorem
Work done by the force $$=$$ change in kinetic energy
i.e., $$w=\Delta K$$
$$w={K}_{2}-{K}_{1}=3-0$$
Work done $$($$w$$)=3$$ joule

Physics

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