## Quick Reference

When all the forces acting on a system are conservative forces, *E*_{k}+*E*_{p} = constant, where *E*_{k} is the kinetic energy and *E*_{p} is the potential energy. This fact is known as the energy equation or the principle of conservation of energy.

From the equation of motion *m***a**=**F** for a particle with mass *m* moving with acceleration **a**, it follows that *m***a. v**=**F. v** and hence (*d*/*dt*)(½*m***v. v**)=**F. v**. When **F** is a conservative force, the energy equation follows by integration with respect to *t*.

*Subjects:*
Psychology — Mathematics.