The equation v² − u² = 2as
(Final velocity)² − (initial velocity)² = 2 × acceleration × distance. In symbols, v² − u² = 2 a s. Here v and u are in metres per second (m/s), a is in metres per second squared (m/s²) and s is in metres (m). All six GCSE physics and combined science specifications treat it as a given equation, so it sits on the sheet in your exam paper.
Equation
v² − u² = 2 a s
| Symbol | Quantity | Unit |
|---|---|---|
v | speed | m/s |
u | initial velocity | m/s |
a | acceleration | m/s² |
s | distance | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet | v² − u² = 2 a s |
| AQA Combined Science (8464) | Given on the sheet | v² − u² = 2 a s |
| Edexcel Physics (1PH0) | Given on the sheet | v² − u² = 2 a x |
| Edexcel Combined Science (1SC0) | Given on the sheet | v² − u² = 2 a x |
| OCR Gateway Physics A (J249) | Given on the sheet | v² − u² = 2 a s |
| OCR Twenty First Century Physics B (J259) | Given on the sheet | v² − u² = 2 a s |
Calculator: v² − u² = 2 a s
When to pick this equation
People call this a SUVAT equation, after the letters s, u, v, a and t. It links speeds, acceleration and distance, and it leaves out time. So reach for it when a question never mentions how long something took.
A typical case: a car brakes from 20 m/s to a stop, and you want the stopping distance. Or a stone falls 5 m, and you want its speed as it hits the ground. In both, time is missing, and this equation fills the gap.
The acceleration must stay the same the whole way. A falling stone with little air resistance is close enough. A skydiver who reaches a steady speed is a different story, because the acceleration changes.
If you study A level maths or physics, the Projectile Motion game on our sister site uses the same equations in two directions at once.
The letters, board by board
Every board keeps v for the final velocity and u for the initial velocity. The letter for distance is where they split.
- AQA (8463 and 8464): v² − u² = 2 a s.
- Edexcel (1PH0 and 1SC0): v² − u² = 2 a x, with x for distance.
- OCR Gateway (J249) and OCR Twenty First Century (J259): v² − u² = 2 a s.
None of the six specifications marks it as Higher tier, so Foundation papers can use it too. Each one files it under the equations you select and apply. Since 2025 the exam papers also print every recall equation, so on the day you get the lot. Compare the full lists on the physics equation sheet page or on the Edexcel equation list.
Rearranged forms
Most questions ask for one of these three:
- v = √(u² + 2 a s)
- a = (v² − u²) ÷ 2s
- s = (v² − u²) ÷ 2a
If the object starts from rest, u is zero and the equation shrinks to v² = 2 a s. For a dropped object, the acceleration is g. Our examples use g = 9.8 m/s², which is the same number as 9.8 N/kg. Use whatever value your question states.
You can also get the same speed from energy. Set the gravitational potential energy lost equal to the kinetic energy gained, and the mass cancels out.
Worked examples
v
- Change the drop to metres: 80 cm = 0.8 m
- v² = u² + 2 a s
- v² = 0² + 2 × 9.8 × 0.8 = 15.68
- v = √15.68
- v = 3.96 m/s (3 s.f.)
3.96 m/s
s
- s = (v² − u²) ÷ 2a
- s = (10² − 4²) ÷ (2 × 1.5)
- s = (100 − 16) ÷ 3
- s = 84 ÷ 3
- s = 28 m
28 m
a
- Change the distance to metres: 0.12 km = 120 m
- a = (v² − u²) ÷ 2s
- a = (18² − 6²) ÷ (2 × 120)
- a = (324 − 36) ÷ 240 = 288 ÷ 240
- a = 1.2 m/s²
1.2 m/s²
Common mistakes
- Subtracting the speeds before you square them. (10 − 4)² is 36, but 10² − 4² is 84, and only the second one fits the equation.
- Mixing up u and v. The starting velocity is u. If a cyclist slows down, u is the bigger number and the acceleration comes out negative.
- Stopping at v². When you solve for final speed, the last step is always a square root.
- Using it when the acceleration changes, such as for a car that speeds up and then cruises. Split the trip into parts first.
Try making s or a the subject of this equation in the Equation Rearranger.
Questions people ask
What does SUVAT stand for?
It lists the five quantities in motion questions: s for displacement, u for initial velocity, v for final velocity, a for acceleration and t for time. This equation uses four of them and drops t.
Why does Edexcel write x instead of s?
It is a choice of letter. Edexcel uses x for distance in several of its equations. Both letters mean the distance moved, so use the one your paper prints.
Can the answer for a be negative?
Yes. A negative acceleration means the object is slowing down. A braking lorry gives a negative a when v is smaller than u.