Adding displacements
When two or more displacements happen along the same straight line, they can be added or subtracted with ordinary arithmetic. Direction is handled by a sign.
1. In the same direction
A child travels 60 m from A to B, then a further 40 m in the same direction, arriving at C.
Total displacement
60 m + 40 m = 100 m
The child is now 100 m from the starting point in a straight line. The distance travelled is 100 m too.
2. In the opposite direction
Now suppose the child travels 60 m from A to B, then instead of going on, comes back 40 m. The direction of that 40 m displacement is opposite to the first, so we take it as negative.
Total displacement
60 m + (−40 m) = 20 m
But the distance travelled is 60 + 40 = 100 m. Distance has no sign, so the return leg adds on.
3. All the way back
What if the child travels the whole way back to where they started?
Total displacement
60 m + (−60 m) = 0
The displacement is zero. That tells us the child is back at the point where the motion began — even though 120 m was travelled.
All three together
| Journey | Distance | Displacement |
|---|---|---|
| 60 m on, then 40 m further on | 100 m | 100 m |
| 60 m on, then 40 m back | 100 m | 20 m |
| 60 m on, then 60 m back | 120 m | 0 |
The difference in short
Distance never decreases. Displacement can decrease, can be zero, and can even be negative.