How fast? Which way?
A cheetah sprints at about 100 km/h. A garden snail creeps at about 0.05 km/h. To describe motion, we need to know how fast something is going, and sometimes which direction it’s moving.
Distance and displacement
| Distance | Displacement |
|---|---|
| The total path travelled | The straight-line change in position from start to finish, with direction |
| Has size only | Has size and direction |
| "I walked 400 m around the track." | "I ended up 0 m from the start." |
If you run once around a 400 m track, your distance is 400 m, but your displacement is 0 m because you finished where you started.
Speed
Speed tells how fast something moves. It’s the distance travelled divided by the time taken:
speed = distance ÷ time
v = d ÷ t
Common units: metres per second (m/s) and kilometres per hour (km/h).
Example: A cyclist travels 3000 m in 600 s. Speed = 3000 ÷ 600 = 5 m/s.
Rearranging the formula
| To find | Use |
|---|---|
| Speed | v = d ÷ t |
| Distance | d = v × t |
| Time | t = d ÷ v |
Example: A car travels at 90 km/h for 2 hours. Distance = 90 × 2 = 180 km.
Converting units
1 m/s = 3.6 km/h
- 10 m/s × 3.6 = 36 km/h
- 72 km/h ÷ 3.6 = 20 m/s
Average and instantaneous speed
- Average speed = total distance ÷ total time. A road trip of 300 km in 4 hours has an average speed of 75 km/h, even though you stopped for lunch and sped up on the highway.
- Instantaneous speed is your speed at one moment, shown on a car’s speedometer.
Velocity
Velocity is speed with a direction.
- Speed: 60 km/h
- Velocity: 60 km/h north
Two cars can have the same speed but different velocities if they’re heading in different directions. A car driving around a circular track at a steady speed has a changing velocity, because its direction keeps changing.
velocity = displacement ÷ time
Some speeds compared
| Object | Approximate speed |
|---|---|
| Snail | 0.001 m/s |
| Walking person | 1.4 m/s (5 km/h) |
| Fastest human sprinter | About 12.4 m/s at top speed (about 44.7 km/h) |
| Cheetah | About 28 m/s (100 km/h) |
| Highway car | About 28 m/s (100 km/h) |
| Commercial jet | About 250 m/s (900 km/h) |
| Sound in air | 343 m/s |
| International Space Station | About 7700 m/s (27 600 km/h) |
| Light | 300 000 000 m/s |
Distance–time graphs
A distance–time graph shows motion.
| Line | Meaning |
|---|---|
| Flat (horizontal) | Not moving |
| Straight, sloping up | Moving at a steady speed |
| Steeper line | Faster speed |
| Curving upward | Speeding up |
The slope (steepness) of the line equals the speed.
Acceleration
Acceleration is how quickly velocity changes.
acceleration = change in velocity ÷ time
Example: A car goes from 0 to 20 m/s in 5 s. Acceleration = 20 ÷ 5 = 4 m/s².
An object accelerates when it speeds up, slows down or changes direction.
Common mistakes
- Using speed and velocity as the same thing. Velocity includes direction.
- Forgetting units. "Speed = 5" means nothing without m/s or km/h.
- Thinking average speed is the average of the top and lowest speeds. It’s total distance ÷ total time.
Try it yourself
- Measure out 20 m. Time yourself walking, then running. Calculate your speed for each in m/s and km/h.
- A train travels 240 km in 3 hours. What’s its average speed?
- How long does it take to cycle 15 km at 20 km/h?
- Draw a distance–time graph for a walk to school with a stop at a crosswalk.
(Answers: 80 km/h; 0.75 h = 45 minutes)
Quick recap
- Distance is the path travelled; displacement is the change in position with direction.
- Speed = distance ÷ time.
- Velocity is speed with direction.
- Average speed covers a whole trip; instantaneous speed is at one moment.
- Acceleration is the rate of change of velocity.