Velocity can change in magnitude, direction or both. Acceleration describes how velocity changes with time.

Over a finite interval, the average acceleration is

$$\bar a=\frac{\Delta v}{\Delta t}.$$

Sign and motion

The sign of acceleration does not by itself tell whether an object is speeding up or slowing down.

If velocity and acceleration have the same sign in one dimension, the speed increases. If they have opposite signs, the speed decreases.

For example, an object moving in the negative direction with negative acceleration is speeding up even though both quantities are negative.

Velocity-time graph

On a graph of velocity against time, average acceleration is the slope between two points.

A horizontal velocity-time graph has zero acceleration. A straight rising or falling line represents constant acceleration.

Instantaneous acceleration

Average acceleration refers to a finite time interval. The rate of change at one particular instant is obtained by taking the limiting slope of the velocity-time graph and is treated as instantaneous acceleration.