Motion in a straight line
distanceNumerical description of how far apart two things are. For example, the distance from Edinburgh to Glasgow is approximately 50 miles. is how far an object moves. It does not include an associated direction, so distance is a scalarA quantity that requires only a size, for example, distance travelled is 20 m. quantity.
speedThe distance travelled in a known time period, eg miles per hour or kilometres per hour. is the rate of changeThe amount of change in the size of a quantity each second. of distance – it is the distance travelled per unit of time. Like distance, speed also does not have an associated direction, so it is a scalar quantity.
Typical speeds
When people walk, run, or travel in a car their speed will change. They may speed up, slow down or pause for traffic.
Some typical values for speed in metres per second (m/s) include:
| Method of travel | Typical speed (m/s) |
| Walking | 1.5 |
| Running | 3 |
| Cycling | 6 |
| Car | 13 - 30 |
| Train | 50 |
| Aeroplane | 250 |
| Method of travel | Walking |
|---|---|
| Typical speed (m/s) | 1.5 |
| Method of travel | Running |
|---|---|
| Typical speed (m/s) | 3 |
| Method of travel | Cycling |
|---|---|
| Typical speed (m/s) | 6 |
| Method of travel | Car |
|---|---|
| Typical speed (m/s) | 13 - 30 |
| Method of travel | Train |
|---|---|
| Typical speed (m/s) | 50 |
| Method of travel | Aeroplane |
|---|---|
| Typical speed (m/s) | 250 |
It is not only moving objects that have varying speed. The speed of the wind and the speed of sound also vary. A typical value for the speed of sound in air is about 330 m/s. A light breeze moves at perhaps 3 m/s, but a gale would be more than 20 m/s.
Calculations involving space, distance and time
The speed of an object can be calculated using the equation:
\( (average) \ speed = \frac{distance \ travelled}{time \ taken} \)
\( v = \frac{x}{t} \)
The distance travelled by an object moving at constant speed can be calculated using the equation:
distance travelled = average speed × time taken
\( x = v \ t \)
This is when:
- distance travelled (x) is measured in metres (m)
- speed (v) is measured in metres per second (m/s)
- time taken (t) is measured in seconds (s)
Learn more on displacement, distance and speed in this podcast
Listen to the full series on BBC Sounds.
Example
A car travels 500 m in 50 s, then 1,500 m in 75 s. Calculate its average speed for the whole journey.
First calculate total distance travelled (x):
500 + 1,500 = 2,000 m
Then calculate total time taken (t):
50 + 75 = 125 s
Then find (v):
\(v = \frac{x}{t}\)
\(v = 2000 ÷ 125\)
\(v = 16 m/s\)
Measuring speeds in the lab
To calculate the speed of an object two measurements are needed:
- how far it travels
- the time it takes to move that distance
These measurements can be made using different types of equipment:
| Equipment | Distance measurement | Time measurement |
| Ruler and stopwatch | Ruler measures distance travelled | Stopwatch measures time taken |
| Light gates | Size of object, measured with a ruler | Light gate connects to a timer, which gives the reading |
| Video analysis | Distance moved from frame to frame observed on a ruler in the pictures | The time between frames is known |
| Equipment | Ruler and stopwatch |
|---|---|
| Distance measurement | Ruler measures distance travelled |
| Time measurement | Stopwatch measures time taken |
| Equipment | Light gates |
|---|---|
| Distance measurement | Size of object, measured with a ruler |
| Time measurement | Light gate connects to a timer, which gives the reading |
| Equipment | Video analysis |
|---|---|
| Distance measurement | Distance moved from frame to frame observed on a ruler in the pictures |
| Time measurement | The time between frames is known |