Calculating Uniform Acceleration (AQA GCSE Physics: Combined Science)

• 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

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