First, derive the work-energy theorem in Newtonian physics:

F=dp/dt

=m(dv/dt)

=m(dv/dx)(dx/dt)

=m(dv/dx)v

Rearranging,

Fdx=mvdv

Integrating,

W=∫Fdx=m∫vdv=½mv_{2}^{2}-½mv_{1}^{2}=ΔK.