Acceleration formula: a = (v − u)/t
Acceleration = change in velocity ÷ time taken. In symbols, a = (v − u)/t, where a is acceleration in metres per second squared (m/s²), v is the final velocity and u the starting velocity, both in m/s, and t is the time in seconds (s). It is a recall equation for all three boards and appears on every board's exam sheet.
Equation
a = Δv ÷ t
| Symbol | Quantity | Unit |
|---|---|---|
a | acceleration | m/s² |
Δv | change in velocity | m/s |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | a = Δv/t |
| AQA Combined Science (8464) | Recall | a = Δv/t |
| Edexcel Physics (1PH0) | Recall | a = (v − u)/t |
| Edexcel Combined Science (1SC0) | Recall | a = (v − u)/t |
| OCR Gateway Physics A (J249) | Recall | a = (v − u)/t |
| OCR Twenty First Century Physics B (J259) | Recall | a = (v − u)/t |
Calculator: a = Δv ÷ t
What acceleration measures
Acceleration is how quickly velocity changes. An acceleration of 3 m/s² means the velocity goes up by 3 m/s every second. From a standing start, that is 3 m/s after one second, 6 m/s after two and 9 m/s after three.
The unit m/s² looks strange. Read it as metres per second, per second. The first part is the velocity. The second part says how often it changes by that amount.
Slowing down counts too. If a cyclist brakes from 8 m/s to 2 m/s, v − u is negative, so the acceleration is negative. Many people call this a deceleration and quote it as a positive number, so read the question with care.
The printed forms
- AQA (8463 and 8464): a = Δv/t. The triangle Δ (delta) means change in, so Δv is the change in velocity.
- Edexcel (1PH0 and 1SC0): a = (v − u)/t.
- OCR Gateway (J249): a = (v − u)/t.
- OCR Twenty First Century (J259): a = (v − u)/t, with the words change in speed ÷ time taken.
Δv and v − u mean the same thing: final velocity minus starting velocity. Each specification places this equation on its recall list. For exam papers from 2025, the boards print recall and given equations together on one sheet, which the physics equation sheet page describes. The OCR Gateway list shows the J249 wording.
Rearranging it
- v = u + a t
- u = v − a t
- t = (v − u) ÷ a
The first of these is handy. It gives the final velocity straight away when you know how hard something accelerates and for how long.
Acceleration links to other pages on this site. A resultant force causes it, through the force equation. When a question gives a distance instead of a time, you need the equation v² − u² = 2as. For steady motion with no acceleration, the speed equation is enough.
Worked examples
a
- Change the final speed to m/s: 72 ÷ 3.6 = 20 m/s
- a = (v − u) ÷ t
- a = (20 − 0) ÷ 8
- a = 2.5 m/s²
2.5 m/s²
t
- t = (v − u) ÷ a
- t = (12 − 30) ÷ (−0.6)
- t = −18 ÷ −0.6
- t = 30 s
30 s
v
- v = u + a t
- v = 0 + 9.8 × 1.5
- v = 14.7 m/s
14.7 m/s
Common mistakes
- Dividing the final velocity by the time and ignoring the starting velocity. A car going from 10 m/s to 16 m/s in 3 s gains only 6 m/s, so a is 2 m/s², not 5.3 m/s².
- Writing u − v instead of v − u. The order matters: final minus start. Swapping them flips the sign and turns a speeding car into a braking one.
- Keeping km/h in the equation. A speed in km/h with a time in seconds gives a number that means nothing.
- Writing the unit as m/s. Acceleration is a rate of change of velocity, so it needs the extra per second: m/s².
Make t or v the subject against the clock in the Equation Rearranger.
Questions people ask
Can something move fast with zero acceleration?
Yes. A plane cruising at a steady 250 m/s in a straight line has zero acceleration. Acceleration is about change, so steady motion gives none.
How do I find acceleration from a graph?
On a velocity against time graph, the gradient is the acceleration. Pick two points on a straight section and divide the rise in velocity by the time between them.