Acceleration

In short: Acceleration is how quickly velocity changes: $a=\frac{v-u}{t}$, measured in m/s². Speeding up, slowing down and changing direction are all acceleration, and near Earth a falling object accelerates at about 9.8 m/s².

What is acceleration?

Acceleration is how quickly velocity changes. It tells you how much the velocity goes up (or down) every second.

$$a=\frac{\text{change in velocity}}{\text{time taken}}=\frac{v-u}{t}$$

• $u$ = starting (initial) velocity
• $v$ = final velocity
• $t$ = time taken
• $a$ = acceleration

Unit: metres per second per second, written m/s² (or m s⁻²).

An acceleration of 3 m/s² means the velocity increases by 3 m/s every second.

Slowing down

When an object slows down, $v$ is smaller than $u$, so the acceleration comes out negative. This is often called deceleration.

Acceleration includes changing direction

Because velocity is a vector, changing direction also counts as acceleration, even if speed stays the same. A car going round a bend at a steady speed is accelerating towards the centre of the bend.

Acceleration due to gravity

Near Earth's surface, anything falling freely (with no air resistance) speeds up by about 9.8 m/s every second. We call this $g$.

$$g\approx 9.8{\text{ m/s}}^2$$

In some exams you may be told to use $g=10{\text{ m/s}}^2$ to make the maths easier. Read the question.

Using the formula three ways

$$a=\frac{v-u}{t}v=u+att=\frac{v-u}{a}$$

Quick summary

• Acceleration is the rate of change of velocity: $a=\frac{v-u}{t}$.
• Unit: m/s². A value of 2 m/s² means velocity changes by 2 m/s each second.
• Negative acceleration means slowing down (if moving in the positive direction).
• Changing direction is also acceleration.
• Free fall near Earth: $g\approx 9.8{\text{ m/s}}^2$, the same for every mass if there is no air resistance.
• $v=u+at$ finds the final velocity.

Quiz