Calculating Uniform Acceleration

Uniform acceleration is constant acceleration
The following equation applies to objects moving with uniform acceleration:

(final speed)² = (initial speed)² + (2 × acceleration × distance moved)

v² = u² + 2as

Where:
- s = distance moved in metres (m)
- u = initial speed in metres per second (m/s)
- v = final speed in metres per second (m/s)
- a = acceleration in metres per second squared (m/s²)

This equation is used to calculate quantities such as initial or final speed, uniform acceleration, or distance moved in cases where the time taken is not known

Examiner Tip

This is an example of an equation that cannot be rearranged with a formula triangle. It is really important that you learn to rearrange equations without the help of a triangle for your exam.

To rearrange any equation, follow these simple rules:

What ever you do to the equation, you must do to both sides
To undo an operation, perform the opposite operation
- To undo a subtraction, you must add (and vice versa)
- To undo a multiplication, you must divide (and vice versa)
- To undo a square, you must square root (and vice versa)

Always show your working out, there is usually a mark awarded for rearranging an equation in an exam question.

Worked example

A car accelerates steadily from rest at a rate of 2.5 m/s² up to a speed of 16 m/s.

Calculate how far the car moves during this period of acceleration.

Answer:

Step 1: List the known quantities

Initial speed,
- Because the car starts from rest
Final speed, $v = 16 m / s$
Acceleration, $a = 2.5 m / s$

Step 2: Identify and write down the equation to use

The question says that the car 'accelerates steadily' - so the equation for uniform acceleration can be used:

$v^{2} = u^{2} + 2 a s$

Step 3: Rearrange the equation to work out the distance moved

Subtract $u^{2}$ from each side

$v^{2} - u^{2} = 2 a s$

Divide both sides by $2 a$

$s = \frac{v^{2} - u^{2}}{2 a}$

Step 4: Substitute known quantities into the equation and simplify where possible

$s = \frac{16^{2} - 0^{2}}{2 \times 2.5}$

$s = \frac{256}{5}$

$s = 51 m$

Examiner Tip

Writing out your list of known quantities and labelling the quantity you need to calculate is really good exam technique. It helps you determine the correct equation to use, and sometimes examiners award credit for showing this working.

Calculating Uniform Acceleration (Edexcel IGCSE Physics: Double Science)

Revision Note