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A body of mass $$'m'$$ starting from is acted on by a force producing a velocity $$v=\sqrt {k \times s}$$ where $$k$$ is a constant and $$s$$ is displacement .The work done by the force in the first $$'t'$$ seconds is:


A
m2 k2 t2/8
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B
m k2 t2/4
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C
m k2 t2/8
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D
m2 k2 t/4
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Solution

The correct option is C $$m\ k^{2}\ t^{2}/8$$
$$v=\sqrt{k\times s}$$
$$\dfrac{ds}{dt}=\sqrt {k\times s}$$
on integration we get
$$s=\dfrac{kt^2}{4}$$
differentiating with respect to t
$$v=\dfrac{kt}{2}$$
differentiating with respect to t
$$a=\dfrac{k}{2}$$
W=Fs=$$\dfrac{mk^2t^2}{8}$$

Physics

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