Displacement, velocity and acceleration
Displacement, velocity and acceleration are vectors: each has a direction as well as a size, unlike the distance and speed used at a lower level.
Practise this conceptDisplacement, velocity and acceleration are the vector upgrades of distance, speed and — well, acceleration doesn't really have a scalar cousin, but the same idea applies. Each one tracks not just how much but which way.
A car that drives 3 km east then 3 km west back to its starting point has covered a distance of 6 km, but its displacement is zero — it ended up exactly where it began. Distance only ever grows; displacement can shrink, cancel out, or even come back to zero.
Acceleration is any change in velocity, not just a change in speed. An object moving at constant speed around a circular track is accelerating the whole time, because its direction is constantly changing even though its speed never does. This is the detail that trips people up most: "constant speed" does not mean "constant velocity," and it certainly doesn't mean "zero acceleration."
Key ideas
Requires: Speed and motion, Scalars and vectors
Unlocks: Newton's first law, Newton's second law
Formulas
| Symbol | Name | Unit |
|---|---|---|
| velocity | m/s (metre per second) | |
| velocity | m/s (metre per second) | |
| acceleration | m/s^2 (metre per second squared) | |
| time | s (second) |
Common misconceptions
- Displacement and distance are always equal in magnitude.
- An object with zero velocity cannot be accelerating.
- If velocity is constant, the object must have some acceleration keeping it that way.