🚗 Kilometres per hour
Car speedometers and road signs in many countries use km/h. It is still a distance divided by a time: kilometres moved in each hour. If a question gives km and hours and asks for km/h, you can divide without converting.
Movement and Position » Speed, Distance and Time
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 1.1, 1.4
- What average speed means and the equation that links it to distance moved and time taken
- How to rearrange the equation to find a distance or a time
- The units to use: metre (m), second (s) and metre/second (m/s)
- How to convert kilometres, minutes, hours and km/h before you calculate
What is average speed?
Speed tells you how fast something is moving. It is the distance an object moves in each unit of time. A sprinter who covers 10 metres every second is faster than a walker who covers 1.5 metres every second.
On a real journey the speed keeps changing. A bus pulls away slowly, speeds up, slows for a junction and stops at a red light. We do not usually know its speed at every moment. What we can easily measure is the total distance it moved and the total time it took. From those two measurements we work out one single value for the whole journey, called the average speed.
Key terms:
- Distance moved: how far the object has travelled in total. Measured in metres (m).
- Time taken: how long the journey lasted. Measured in seconds (s).
- Average speed: the distance moved divided by the time taken. Measured in metres per second (m/s).
The unit m/s is read as "metres per second". A speed of 8 m/s means the object moves 8 metres in every second, on average.
The metre, the second and the metre/second are the first three units of this section of the course. You will meet the others in later lessons: the metre/second2 (m/s2), the newton (N), the kilogram (kg) and the newton/kilogram (N/kg).
The equation you must learn
Learn this equation
average speed = distance moved ÷ time taken
This equation is not given in the exam. You must know it by heart and be able to use it.
Every calculation follows the same three steps. Write the equation. Put the numbers in. Then write the answer with its unit.
Worked example 1: finding average speed
A runner moves 100 m in 12.5 s. Calculate her average speed.
average speed = distance moved ÷ time taken
average speed = 100 ÷ 12.5
average speed = 8 m/s
She was slower than this at the start and faster near the end. 8 m/s is the average for the whole run.
Rearranging the equation
The same equation can be turned round to find the distance moved or the time taken. You need all three forms.
🏃 To find speed
average speed = distance moved ÷ time taken
📏 To find distance
distance moved = average speed × time taken
⏰ To find time
time taken = distance moved ÷ average speed
A quick check helps you pick the right one. A faster object, or one moving for longer, goes further, so distance comes from multiplying. A faster object takes less time to cover the same distance, so to find time you divide by the speed.
Worked example 2: finding distance
A cyclist rides at an average speed of 6 m/s for 5 minutes. Calculate the distance moved.
First change the time into seconds: 5 minutes = 5 × 60 = 300 s
distance moved = average speed × time taken
distance moved = 6 × 300
distance moved = 1800 m
Worked example 3: finding time
A girl walks 2.4 km to the shops at an average speed of 1.5 m/s. Calculate the time taken.
First change the distance into metres: 2.4 km = 2.4 × 1000 = 2400 m
time taken = distance moved ÷ average speed
time taken = 2400 ÷ 1.5
time taken = 1600 s
That is just under 27 minutes, which is a sensible time for a walk of that length.
Getting the units right
To get an answer in m/s, the distance must be in metres and the time must be in seconds. Exam questions often give kilometres, minutes or hours instead, so convert before you calculate.
| To change | Do this | Example |
|---|---|---|
| kilometres to metres | multiply by 1000 | 3.5 km = 3500 m |
| minutes to seconds | multiply by 60 | 4 minutes = 240 s |
| hours to seconds | multiply by 3600 | 2 hours = 7200 s |
| km/h to m/s | divide by 3.6 | 72 km/h = 20 m/s |
| m/s to km/h | multiply by 3.6 | 10 m/s = 36 km/h |
There are 3600 seconds in an hour because 60 minutes × 60 seconds = 3600.
🔬 Metres per second
Physics uses m/s. Where does 3.6 come from? An object moving at 1 m/s covers 3600 m in an hour, which is 3.6 km. So 1 m/s = 3.6 km/h.
Worked example 4: one journey, two units
A car travels 90 km in 1.25 hours. Calculate its average speed in km/h and in m/s.
In km/h: average speed = distance moved ÷ time taken = 90 ÷ 1.25 = 72 km/h
In m/s: distance moved = 90 × 1000 = 90 000 m. Time taken = 1.25 × 3600 = 4500 s.
average speed = 90 000 ÷ 4500 = 20 m/s
Check: 72 ÷ 3.6 = 20 m/s. Both methods agree.
Common mistakes
- Not converting units. Dividing kilometres by minutes gives km per minute, not m/s. Change to metres and seconds first.
- Dividing the wrong way round. It is always distance on top, time underneath. Speed is never time ÷ distance.
- Multiplying minutes by 100. There are 60 seconds in a minute, so 2.5 minutes is 150 s, not 250 s.
- Leaving out the unit. An answer of "20" could mean anything. Write 20 m/s.
- Forgetting stops. The time taken is the whole time for the journey, including any time spent standing still.
Exam-style question
A train travels between two stations. The distance between the stations is 5.4 km and the journey takes 3 minutes.
(a) State the equation linking average speed, distance moved and time taken. [1 mark]
(b) Calculate the average speed of the train in m/s. [3 marks]
(c) The train then passes through a tunnel that is 750 m long at the same average speed. Calculate the time taken to move a distance of 750 m. [2 marks]
(d) Explain why the speed calculated in (b) is called an average speed. [1 mark]
Model answer
(a) average speed = distance moved ÷ time taken (1)
(b) distance moved = 5.4 × 1000 = 5400 m and time taken = 3 × 60 = 180 s (1)
average speed = 5400 ÷ 180 (1)
average speed = 30 m/s (1)
(c) time taken = distance moved ÷ average speed = 750 ÷ 30 (1)
time taken = 25 s (1)
(d) The speed of the train changes during the journey, because it speeds up as it leaves one station and slows down to stop at the next, so 30 m/s is the value for the whole journey and not its speed at every moment. (1)
Exam tip
In a "calculate" question, do the unit conversions on their own line before you touch the equation, as in part (b). If your final answer is wrong, the examiner can still give you marks for the correct conversions and substitution that they can see.
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