Distance is the total length of the path travelled, whereas displacement is the change in position from the initial point to the final point, including direction. Distance is a scalar; displacement is a vector.
The Reasoning
This distinction is part of IB Physics A.1 Kinematics and applies at both SL and HL.
| Quantity | Distance | Displacement |
|---|---|---|
| Type | Scalar quantity: magnitude only | Vector quantity: magnitude and direction |
| Meaning | Total path length travelled | Change in position |
| Possible values | Zero or positive | Positive, negative, or zero in one dimension |
| Depends on | The route taken | Initial and final positions only |
| SI unit | metre (m) | metre (m) |
In one-dimensional motion, displacement is calculated using
The sign follows the chosen positive direction. A negative displacement does not mean the object travelled a negative distance; it means the final position lies in the negative direction relative to the initial position.
Worked Example
A student walks east and then west.
- Distance:
- Displacement: east
If the student instead walks east and then west, the distance is , but the displacement is zero because the final and initial positions are identical.
Two useful consequences follow. For a journey that returns to its starting point, displacement is zero even though distance is not. For motion without any reversal of direction, distance equals the magnitude of displacement.
A common misconception is that distance and displacement are interchangeable because both use metres. They are not: identical units do not mean identical physical quantities. The magnitude of displacement can never exceed the distance travelled.
IB Exam Technique
For calculations, define a positive direction before assigning signs. On a velocity versus time graph, displacement is the signed area between the graph and the time axis, while distance is the sum of the magnitudes of all areas. In an Explain response, state both the scalar/vector distinction and the path-versus-position distinction.
