The relation between the displacement x and the time t for a body of mass 2kg moving under the action of force is given by x=t^{3}/3 , where x is in metre and t in second , calculate the work done by body in first 2 seconds.

Here,

Mass, m = 2 kg

Displacement is given as, x = t^{3}/3

So, d(x)/dt = (3)(t^{2})/3 = t^{2}

=> d^{2}(x)/dt^{2} = 2t

=> a = 2t

This is the acceleration of the body.

Now,

For a small displacement ‘dx’ the work done is,

dW = F.dx

=> dW = (ma).d(t^{3}/3)

=> dW = 2(2t)(3t^{2}/3)

=> dW = 4t^{3}

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