When all the forces acting on a system are conservative forces, Ek+Ep = constant, where Ek is the kinetic energy and Ep is the potential energy. This fact is known as the energy equation or the principle of conservation of energy.
From the equation of motion ma=F for a particle with mass m moving with acceleration a, it follows that ma. v=F. v and hence (d/dt)(½mv. v)=F. v. When F is a conservative force, the energy equation follows by integration with respect to t.
Subjects: Psychology — Mathematics.