(3-10)    Begin with the idea that the work W done on an object equals the amount of kinetic energy (Ek) imparted to it as a result.  So we can write:   

Now, we can bring in the expression we derived earlier (see question 3-1) for the force:          F = (dp/dt).

①  Substitute this into the kinetic energy expression and then rewrite it using the classical definition, p = mv.

②  Rearrange this expression to make it an integration with respect to dv.  Think about what (dx/dt) means and rewrite the integral accordingly.

③  Calculate the definite integral and hence find the expression for the classical kinetic energy.