Movement & Position
Forces & Motion
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
Common exam question
Using v² = u² + 2as when the time is not given
Question: Calculate a speed after a fall from rest, a distance needed to slow down, or an acceleration over a braking distance, with no time given (3–4 marks).
Set in 8 of the 24 papers. The marks are substitution, rearrangement and evaluation, so substitute before you rearrange. Square the speeds before subtracting: subtracting the two speeds, or using change in speed × time, was rejected as wrong physics. "From rest" means u = 0 and "comes to rest" means v = 0; one scheme credited u = 0 and refused the substitution mark for v = 0. A deceleration is substituted as negative; the sign of the final answer is ignored. For free fall use g = 10 m/s², as the paper says (9.8 or 9.81 is also accepted). From a stopping-distance graph, use the braking distance, not the whole stopping distance; and when a number of significant figures is asked for, that rounding is a separate mark.
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