Scalars and Vectors
Scalar quantities have magnitude (size) only. Vector quantities have magnitude AND direction.
| Scalar | Vector |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| Mass | Force |
| Time | Acceleration |
| Temperature | Momentum |
Distance
Distance is the total length of the path travelled, no matter the direction.
A runner who jogs 400 m around a track has travelled a distance of 400 m.
- Symbol: d or s
- Unit: metre (m)
- Scalar quantity
Displacement
Displacement is the straight-line distance from start to finish, including direction.
If the runner starts and ends at the same point after one lap, their displacement is 0 m.
- Symbol: s or x
- Unit: metre (m), with a direction
- Vector quantity
A person walks 3 m East and 4 m North. Their distance = 7 m. Their displacement = 5 m (North-East), calculated using Pythagoras: m.
Comparing Distance and Displacement
| Situation | Distance | Displacement |
|---|---|---|
| Walk 10 m East | 10 m | 10 m East |
| Walk 10 m East, then 10 m West | 20 m | 0 m |
| Walk 3 m North, 4 m East | 7 m | 5 m (NE) |
Real world: Running a lap around a track
An athlete runs one complete 400 m lap around a stadium track and finishes exactly where they started.
- Distance = 400 m (the total path length run)
- Displacement = 0 m (start and finish are the same point)
The athlete definitely moved — but there is no net displacement.
Real world: Daily school commute
A student walks 1.2 km east to school, then at the end of the day walks 1.2 km west back home.
- Distance = 1.2 + 1.2 = 2.4 km
- Displacement = 0 km (back at home — the starting point)
If they only walk to school (one way): distance = displacement = 1.2 km east.
Real world: GPS navigation vs. odometer
A car drives through a winding city route: 3 km north, 4 km east, then arrives at a destination.
- Odometer (distance): records 3 + 4 = 7 km driven
- GPS displacement: straight-line from start to finish = (north-east)
GPS shows you the displacement; the odometer shows the distance.
Where do you see this in real life? Your phone's fitness tracker counts steps to measure total distance walked. But a GPS app calculates your displacement — the straight-line distance from where you started to where you are now. These can be very different for a hike with lots of twists and turns.
Practice Problems
A student walks 6 m North, then 6 m South. What is the distance? What is the displacement?
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Is speed a scalar or vector? What about velocity?
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A car travels 30 m East and 40 m North. Calculate the displacement.