A locomotive of mass \(m\) starts moving on the \(x\)-axis from the origin such that its velocity (v) is directly proportional to the square root of its displacement; \(v=k\sqrt{x}\). Find the total work done by all of the forces acting on the locomotive in the first \(t\) seconds of its motion.

The answer will be a function \(f(m,k,t)\) and the constant of proportionality which relates the velocity and the square root of the displacement. Find the sum of the exponents on \(m,k,\) and \(t\) in the function \(f\).

PS: In fact, there is a much shorter way to solve this problem, one which requires only two steps. If you can figure it out, put it down as a solution. This alternative solution does not require calculus or any difficult mathematics. It simply requires you to see the problem which I have given in a little more detail

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