A.1.2—Velocity and acceleration rates

Velocity is a rate

Velocity is the rate of change of position:

$$\vec v=\frac{d\vec r}{dt}$$

Over a finite interval, average velocity is displacement divided by elapsed time.

Acceleration changes velocity

Acceleration is the rate of change of velocity:

$$\vec a=\frac{d\vec v}{dt}$$

A constant acceleration gives equal changes in velocity during equal time intervals.

Read the gradient

On a position–time graph, the gradient represents velocity. On a velocity–time graph, the gradient represents acceleration. The graph’s slope, not its height alone, carries the rate-of-change meaning.

Common trap

Distance divided by time gives average speed, not instantaneous velocity. Likewise, a large velocity does not imply a large acceleration unless the velocity is changing rapidly.