4PH1

Movement & Position

Forces & Motion · 1 question type

Practise

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 12% of your exam marks.

stable
High
Stable12%

Distance-time graphs, speed calculations and velocity appear in nearly every series.

When to reach for v² = u² + 2as

  • Uniform acceleration means the acceleration is constant throughout the motion
  • When you know any three of (initial speed, final speed, acceleration, distance) but not the time, the following equation links them in one line:

v² = u² + 2as

  • where:
    • u = initial speed (m/s)
    • v = final speed (m/s)
    • a = acceleration (m/s²)
    • s = distance moved (m)
  • All four quantities must be in SI units before substituting

Rearranging without a triangle

  • Formula triangles only work for simple multiply/divide equations; v² = u² + 2as contains a square and a sum, so triangles are no help
  • Use ordinary algebra: subtract u² from both sides, divide both sides by 2a, or take a square root, depending on which letter is the subject. Whatever you do to one side, do to the other
Worked example

Using v² = u² + 2as to find braking distance

A vehicle travelling at 20 m/s brakes to rest with a deceleration of 5 m/s². Find the braking distance.

Solution:

  • Identify known quantities: u = 20 m/s, v = 0 m/s, a = −5 m/s²
  • Substitute into v² = u² + 2as: 0² = 20² + 2 × (−5) × s
  • Rearrange: 2 × 5 × s = 400, so s = 400 ÷ 10
  • Distance = 40 m