## Quick Reference

A particle is moving with constant speed if the magnitude of the velocity is independent of time. Thus **v. v**=constant and this gives 2 **v.**(*d***v**/*dt*)=0. Hence there are three possibilities: **v**=**0**, or *d***v**/*dt*=**0**, or **v** is perpendicular to *d***v**/*dt*. The third possibility shows that the velocity is not necessarily constant. One such example is when a particle is moving in a circle with constant speed, and then the acceleration is perpendicular to the velocity.

*Subjects:*
Mathematics.