Distance is the total length of the path an object travels. Displacement is how far the object ends up from where it started, in a straight line, together with the direction. The two can be different, and sometimes they are very different.
This lesson closes motion and graphs by adding direction to the ideas from calculating speed over a segment.
How are they different?
| Quantity | Meaning | Has direction? | Can it be zero after a trip? |
|---|---|---|---|
| Distance | Total path length | No | Only if the object never moved |
| Displacement | Straight-line change in position | Yes | Yes, if it returns to the start |
Quantities with both size and direction are called vectors. Quantities with only size are scalars. Distance and speed are scalars; displacement and velocity are vectors.
How do I tell which one a question wants?
- Read the wording. “How far did it travel?” asks for distance. “How far is it from the start?” or “what is its displacement?” asks for displacement.
- Sketch the path as arrows, each labelled with a length and a direction.
- Add lengths for distance.
- Combine arrows for displacement: movements in opposite directions subtract, and movements at right angles need Pythagoras.
- State direction with displacement.
Worked example
An invented walk along a straight path: 60 m east, then 25 m west. The whole walk takes 50 s.
Distance: 60 + 25 = 85 m.
Displacement: the second leg undoes part of the first. 60 − 25 = 35 m east.
Average speed: distance ÷ time = 85 ÷ 50 = 1.7 m/s.
Average velocity: displacement ÷ time = 35 ÷ 50 = 0.7 m/s east.
Both quantities answer a fair question. One describes how much walking happened, the other describes where the walker ended up.
The mistake to watch for
A student asked for the displacement of the walk above adds the two legs.
Mistaken answer: 60 + 25 = 85 m east.
This is the total distance. It also ignores that the second leg went the opposite way.
Correction: draw the two arrows, east then west, and notice that the second reverses part of the first. The displacement is 35 m east, while the distance stays 85 m. For a full lap of a 400 m track, the same idea gives distance 400 m and displacement 0 m.
Check yourself
Try these, then open each answer.
1. A hiker walks 3 km north, then 1 km south. Find the distance and the displacement.
Show answer
Distance = 3 + 1 = 4 km. Displacement = 3 − 1 = 2 km north.
2. A ball is thrown straight up 5 m and caught at the same height from which it was thrown. Find the distance travelled and the displacement.
Show answer
It goes up 5 m and comes down 5 m, so distance = 10 m. It finishes where it started, so displacement = 0 m.
3. A student walks 8 m east and then 6 m north. Find the distance, and the size and direction of the displacement.
Show answer
Distance = 8 + 6 = 14 m. Displacement size = √(8² + 6²) = √100 = 10 m. Its direction is about 37° north of east (since tan⁻¹(6 ÷ 8) ≈ 36.9°).
Where this leads next
With the five lessons complete, test yourself on the motion and graphs practice set, which mixes every skill. The bounds and rounding explainer can help when a question asks how precisely a measured distance is known, and the triangle and bearings reasoning board is useful when movement is at an angle.
If you understand each idea but mix them up in longer questions, a teacher in online one-to-one Physics tuition can practise mixed problems with you.