Average Speed vs Average Velocity
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Walk 4 km to school and back in an hour: average speed 4 km/h, average velocity zero. One uses total distance, the other displacement.
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Key points
- Average speed = total distance ÷ total time (scalar).
- Average velocity = total displacement ÷ total time (vector).
- A round trip has average velocity 0 but a non-zero average speed.
- Never average two speeds directly: 4 and 12 km/h over equal distances give 6, not 8.
- |Average velocity| ≤ average speed.
The surprising walk
A boy walks 2 km to school and 2 km back in 1 hour. Distance = 4 km, so average speed = 4 km/h. He ends where he started, so displacement = 0 and average velocity = 0.
Average speed = total distance ÷ total time; average velocity = total displacement ÷ total time
The trap: averaging two speeds
Going 12 km at 4 km/h takes 3 h; returning 12 km at 12 km/h takes 1 h. Average speed = 24 km ÷ 4 h = 6 km/h, not (4 + 12) ÷ 2 = 8, because more time is spent on the slow leg.
Comparison
| Feature | Average speed | Average velocity |
|---|---|---|
| Uses | Total distance | Displacement |
| Type | Scalar | Vector |
| Zero after moving? | No | Yes (round trip) |
| Relation | ≥ |average velocity| | ≤ average speed |
Try it yourself
Goal: Compare average speed (path length ÷ time) with average velocity (displacement ÷ time) on different paths.
- Pick a path: straight, there-and-back, zig-zag or circle.
- Press Play or drag the time slider to the end.
- Read the average speed and the average velocity.
- On there-and-back and the full circle, see the average velocity fall to zero while the average speed does not.
Quick quiz
5 questions. Choose an answer for each, then submit to see your score and the explanations.
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