Key takeaways
- Acceleration is a = (v − u) ÷ t: change in velocity divided by time.
- Always subtract initial velocity from final velocity, in that order.
- A negative result means the object is slowing down.
- Acceleration is measured in metres per second squared (m/s²).
In this guide
What is acceleration?
Acceleration is the rate at which velocity changes over time. It answers the question: how quickly is something speeding up, slowing down, or changing direction?
Why does acceleration matter?
Two cars can reach the same top speed, but the one that gets there faster has higher acceleration, and that's often what people actually feel and care about.
Going from 5 m/s to 25 m/s in 4 seconds is an acceleration of 5 m/s². Keep that rate up for another 5 seconds from a standing start, and you'd reach 90 km/h.
The formula
| Symbol | What it means | Example |
|---|---|---|
| a | The acceleration, in metres per second squared (m/s²) | 5 m/s² |
| v | The final velocity, in metres per second (m/s) | 25 m/s |
| u | The initial (starting) velocity, in metres per second (m/s) | 5 m/s |
| t | The time taken for that change, in seconds (s) | 4 s |
How to calculate acceleration step by step
- 1Note the starting velocity (u). Measure it in m/s.
- 2Note the final velocity (v). Measure it in m/s.
- 3Subtract u from v.
v − ugives the change in speed. - 4Divide by the time taken.
(v − u) ÷ tgives the acceleration in m/s².
Try the calculator below with your own velocities and time to see every step laid out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing up speed and velocity units. Both v and u need to be in the same unit, usually m/s, before you subtract.
- Missing negative acceleration. If an object slows down, the answer comes out negative, which correctly describes deceleration.
- Forgetting units on time. Time must be in seconds, so convert minutes first if needed.
Tips and tricks
- For a rough estimate, round the velocities to the nearest 5 before subtracting.
- Acceleration is closely linked to force through Newton's second law: F = m × a.
- Once you know your acceleration, multiply by time to find the resulting change in velocity.
Where you'll use it in real life
- Cars: manufacturers advertise 0-to-100 km/h times, which is really an acceleration measurement.
- Braking: measuring how quickly a vehicle slows down (a negative acceleration) is key to road safety testing.
- Sport: sprinters and cyclists are timed and compared partly by how quickly they reach top speed.
- Rides and lifts: engineers keep acceleration within comfortable limits so rides and elevators don't feel jarring.
Quick summary
To find acceleration, subtract the starting velocity from the final velocity, then divide by the time taken. A positive result means speeding up, and a negative one means slowing down. Use the calculator above to work through your own example.
Worked example
A car speeds up from 5 m/s to 25 m/s over 4 seconds while merging onto a highway. What is its acceleration?
- 01a = (v - u) / t
- 02a = (25 - 5) / 4
- 03a = 20 / 4
- 04a = 5 m/s²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate acceleration?
Subtract the initial velocity from the final velocity, then divide by the time taken: a = (v − u) ÷ t. The result is in m/s².
What does negative acceleration mean?
A negative result means the object is slowing down, sometimes called deceleration, rather than speeding up.
What unit is acceleration measured in?
Metres per second squared (m/s²), which describes how much the velocity in m/s changes every second.
What's the difference between velocity and acceleration?
Velocity is how fast something is moving right now. Acceleration is how quickly that velocity is changing over time.
