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.(dv/dt)=0. Hence there are three possibilities: v=0, or dv/dt=0, or v is perpendicular to dv/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.