To find a speed you need a distance. But suppose you walk 5 m east, then 2 m back west. How far did you go? That depends on what the question means. Physics keeps two different answers apart, and a number line shows both.
Key idea
Distance is the total length of the path you traveled; it is never negative. Displacement is the straight change in position from start to finish, with a direction (or a sign).
Why it works
Put the start at 0 and call east positive. Walking 5 m east takes you to $+5$; walking 2 m west takes you to $+3$. You covered $5 + 2 = 7$ m of ground, so the distance is 7 m. But you ended only 3 m east of where you began, so the displacement is $+3$ m. Moves in opposite directions add to the distance but cancel in the displacement.
Worked example: There and partly back
A dog runs 12 m east to fetch a stick, then 4 m west. Find the distance and the displacement.
- Distance: add the lengths, $12 + 4 = 16$ m.
- Displacement: with east positive, $+12 + (-4) = +8$ m.
- So the dog ended 8 m east of where it started.
Answer: Distance 16 m; displacement 8 m east
Worked example: A round trip
A swimmer swims one 50 m length of a pool and back. Find the distance and the displacement.
- Distance: $50 + 50 = 100$ m.
- Displacement: $+50 + (-50) = 0$ m. She is back where she started.
Answer: Distance 100 m; displacement 0 m
Common mistake
Giving the distance walked when the question asks how far from the start you ended up. "How far from the start" means the displacement. Check: picture where you finished on the number line and measure straight back to 0.