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A locomotive of mass m starts moving so that its velocity varies according to the law, v = as where a is a constant and s is the distance covered. Find the total work done by all the forces acting on locomotive during the first t second after the beginning of motion.

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Ds/dt = asqrt(s) s^(-1/2) ds = adt s^(1/2) / (1/2) = at 2sqrt(s) = at s = a^2 t^2 / 4 a = d2s / dt2 = a^2 / 2 dW = F dS = ma dS Since the force is constant, W = ma integral(dS) = ma S = (mk^2 / 2) x (a^2 t^2 / 4)
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