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
Example — a car starts from rest and accelerates uniformly at 4.0 m/s² until it reaches 20 m/s. Calculate the distance it has travelled at that moment.
- List the known quantities: u = 0 m/s; v = 20 m/s; a = 4.0 m/s²
- Substitute into v² = u² + 2as:
20² = 0² + 2 × 4.0 × s
400 = 8.0 s
s = 400 / 8.0 = 50 m