Calculating Acceleration

Acceleration is the change in velocity per unit time. It tells you how quickly an object speeds up, slows down, or changes direction.

What is the equation?

$a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}$

where $a$ is acceleration in m/s², $v$ is the final velocity in m/s, $u$ is the initial velocity in m/s, and $t$ is the time taken in s.

A positive value means the object is speeding up (in the chosen positive direction). A negative value means it is slowing down or accelerating in the opposite direction.

Worked example

A car accelerates from 5.0 m/s to 25.0 m/s in 8.0 s. Calculate the acceleration. [3]

Step 1. Write the equation: $a = \frac{v - u}{t}$

Step 2. Substitute: $a = \frac{25.0 - 5.0}{8.0}$

Step 3. $a = \frac{20.0}{8.0} = 2.5\ \text{m/s}^2$

Marking points: M1 for the equation stated or used correctly. M1 for correct substitution showing $v - u$. A1 for 2.5 m/s² with correct unit.

These marking points are for this original example and are not an official Cambridge mark scheme.

What does the unit m/s² mean?

The unit m/s² means “metres per second, per second”. An acceleration of 2.5 m/s² means the velocity increases by 2.5 m/s every second. After 1 s it has gained 2.5 m/s; after 2 s it has gained 5.0 m/s, and so on.

Common errors and how to correct them

• Using final velocity instead of the change in velocity. Substituting $v$ instead of $v - u$ gives the wrong answer. Always subtract the initial velocity.
• Writing the unit as m/s instead of m/s². Acceleration is not a speed. The squared second in the denominator reflects the “per second” applied twice.
• Defining acceleration as “getting faster”. Examiners reject this. The accepted definition is “change in velocity per unit time.”

How to apply this in an exam

Always write the equation first, then substitute, then calculate. Even with a wrong final answer, stating the equation and substituting correctly typically earns two of the three marks available.