# 5.6.13 Calculating Uniform Acceleration

### Calculating Uniform Acceleration

• The following equation of motion applies to objects moving with uniform (constant) acceleration:

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

v2 = u2 + 2as

• Where:
• s = distance travelled 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, acceleration, or distance travelled in cases where the time taken is not known

#### 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.

Step 1: 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:

v2 = u2 + 2 × a × s

Step 2: List the known quantities

• Initial speed, u = 0 m/s (the car starts from rest)
• Final speed, v = 16 m/s
• Acceleration, a = 2.5 m/s2
• Distance, s = ? (this needs to be calculated)

Step 3: Substitute known quantities into the equation and simplify where possible

162 = 02 + (2 × 2.5 × s)

• This can be simplified to:

256 = 5 × s

Step 4: Rearrange the equation to work out the distance travelled

s = 256 ÷ 5

s = 51.2 m

#### Exam 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. ### Author: Jonathan

Jonathan graduated with a first-class Master's degree in Theoretical Physics from Imperial College London. He has worked in education for more than a decade as a Maths and Physics Teacher, Tutor, Head of Physics, and most recently, as Assistant Headteacher. He is now an Educational Consultant and works with us to design and improve our Physics resources.
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