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=½mv22-½mv12=ΔK.