How fast?

Displacement and distance travelled inform us only on the magnitude of the change in position, but not on the rate of this change. To get a more complete description of motion, we need to define additional quantities.

The same displacement can characterise much faster motion if it takes place in a shorter time interval. The quantity that serves as a measure of this difference is called velocity. First, we shall introduce average velocity, which is a simpler concept and describes the rate of change in position over a longer interval, then we shall refine it and introduce instantaneous velocity. Speed is in the same relation to velocity as the distance travelled is to displacement.

Velocity may also change over time. To quantify this, we shall define acceleration, which is the rate of change of velocity.