Speed, Velocity and Acceleration
Speed, velocity and acceleration explained: scalars vs vectors, formulas, units, reading distance-time and velocity-time graphs, and worked examples.
Key takeaways
- Speed is how fast; velocity is how fast in a given direction.
- Acceleration is the rate of change of velocity: a = (v − u) ÷ t.
- On a velocity–time graph, the slope is acceleration and the area is distance.
On this page
Speed, velocity and acceleration describe motion. They’re often confused, but the differences matter in every physics problem.
Speed
Speed = distance ÷ time, measured in m/s. It’s a scalar: it has size but no direction.
Velocity
Velocity = displacement ÷ time, where displacement is the straight-line change in position with direction. It’s a vector. A car driving around a roundabout at a steady 30 km/h has constant speed but changing velocity.
Acceleration
Acceleration = change in velocity ÷ time
a = (v − u) ÷ t
- u = starting velocity
- v = final velocity
- t = time taken
Units: m/s². Slowing down is sometimes called deceleration, a negative acceleration.
Worked examples
- Speed: a runner covers 400 m in 80 s: speed = 5 m/s.
- Acceleration: a car goes from 0 to 27 m/s in 9 s: a = 27 ÷ 9 = 3 m/s².
Reading graphs
| Graph | Slope means | Area means |
|---|---|---|
| Distance–time | Speed | — |
| Velocity–time | Acceleration | Distance travelled |
A flat line on a distance–time graph means stationary; on a velocity–time graph it means constant velocity.
The equations of motion
For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as. They’re used in our free fall and projectile motion calculators, and they follow from Newton’s second law.
Frequently asked questions
Can an object accelerate at constant speed?
Yes, if its direction changes, as in circular motion; see centripetal force.
Is velocity always positive?
No. Velocity can be negative when an object moves in the opposite direction to the one chosen as positive.
What is the unit of acceleration?
Metres per second squared (m/s²).
Sources
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