When all the forces acting on a system are conservative forces, T + V = constant, where T is the kinetic energy and V is the potential energy. This fact is known as the energy equation or the principle of conservation of energy.

From Newton’s second law, ma = F for a particle with mass m moving with acceleration a, it follows that m a·v = F·v and hence $(\text{d}/\text{d}t)(\frac{1}{2}mv.v)=F.v.$ When F is a conservative force, the energy equation follows by integration with respect to t. See Noether’s theorem, work.