Topic 1 of 6
Distance, speed and velocity
Distance is the total length of the path travelled. Displacement is the change in position from start to finish, including direction.
If you walk 3 m to the right, then 1 m back to the left, you have walked 4 m in total, but finish 2 m to the right of where you started. Your distance is 4 m; your displacement is 2 m to the right.
- Speed
- Distance travelled per unit time. It tells you how fast, without a direction. For example, 2 m/s.
- Velocity
- Rate of change of displacement. It tells you how fast and in which direction. For example, 2 m/s to the right.
Speed is a scalar; velocity is a vector. A scalar has magnitude (size) only, while a vector has magnitude and direction. Along a straight line, choose one direction as positive. Motion in the opposite direction has negative velocity, even though speed is always non-negative.
The time includes any stops. Average speed describes the whole journey; the object does not have to travel at that speed at every instant. Convert units before substituting: 1 minute = 60 s and 1 km = 1000 m. To convert km/h to m/s, divide by 3.6.
Distance in centimetres divided by time in seconds gives cm/s. For example, 30 cm in 2.0 s gives 15 cm/s = 0.15 m/s, because each centimetre is 0.01 m.
Worked example
Average speed including a stop
A student walks 60 m in 40 s, waits for 20 s, then walks another 40 m in 40 s. Find the average speed.
- Add the distances: 60 + 40 = 100 m.
- Include all the time: 40 + 20 + 40 = 100 s.
- Divide: average speed = 100 m / 100 s = 1 m/s.
This means that travelling steadily at 1 m/s for 100 s would cover the same total distance.
Include the whole journey. Add all the distances and all the times, including stops. Taking a simple mean of the speeds only works when the time spent at each speed is equal.