Speed, distance and time are linked by speed = distance ÷ time, which rearranges to distance = speed × time and time = distance ÷ speed. Average speed for a journey is the total distance divided by the total time, including any stops. On a distance–time graph, the gradient is the speed and a horizontal line means the object is stationary.
Speed, distance and time
- Speed = distance ÷ time
- Distance = speed × time; time = distance ÷ speed
- Average speed = total distance ÷ total time
- Distance–time graph: gradient = speed; flat line = stationary
- m/s to km/h: × 3.6; km/h to m/s: ÷ 3.6
The speed formula
Speed tells you the distance travelled per unit of time. A car covering 150 km in 2 hours has an average speed of 150 ÷ 2 = 75 km/h. A formula triangle with distance at the top helps you rearrange: cover the quantity you want and read off the calculation.
Working with minutes
Times in minutes must be converted to hours when the speed is in km/h. 45 minutes is 0.75 hours, not 0.45. If a time comes out as a decimal of an hour, convert back to hours and minutes: 0.75 hours is 45 minutes.
Average speed for a whole journey
Average speed is the total distance divided by the total time, including any time spent stopped. Do not average the separate speeds. For a journey of 100 km in 1.5 hours, a 30-minute stop, then 60 km in 1 hour, the total is 160 km in 3 hours, giving 53.3 km/h.
Distance–time graphs
Time goes along the horizontal axis and distance up the vertical axis. The gradient of each straight section is the speed for that section, a steeper line is faster, and a horizontal line means the object is not moving. A line sloping back down shows the return journey.
Converting speed units
To convert m/s to km/h, multiply by 3.6, because there are 3600 seconds in an hour and 1000 metres in a kilometre. To convert km/h to m/s, divide by 3.6. So 15 m/s is 54 km/h.
Worked examples
Example 1. A car travels 150 km in 2 hours. Work out its average speed.
- Speed = 150 ÷ 2.
Answer: 75 km/h.
Example 2. A coach travels at 64 km/h for 2.5 hours. How far does it travel?
- Distance = speed × time = 64 × 2.5.
Answer: 160 km.
Example 3. A cyclist rides 45 km at 60 km/h. How long does the ride take, in minutes?
- Time = 45 ÷ 60 = 0.75 hours.
- 0.75 × 60 minutes.
Answer: 45 minutes.
Example 4. A driver travels 100 km in 1.5 hours, stops for 30 minutes, then travels 60 km in 1 hour. Work out the average speed for the whole journey.
- Total distance: 160 km. Total time: 1.5 + 0.5 + 1 = 3 hours.
- 160 ÷ 3 = 53.33…
Answer: 53.3 km/h (1 d.p.).
Example 5. Convert 15 m/s into km/h.
- Multiply by 3.6: 15 × 3.6.
Answer: 54 km/h.
Common mistakes
- Treating minutes as decimals of an hour. 45 minutes is 0.75 hours, not 0.45.
- Averaging the speeds. Average speed = total distance ÷ total time.
- Ignoring stops. Time spent stopped counts in the total time.
- Rearranging the formula wrongly. Distance = speed × time; time = distance ÷ speed.
- Converting m/s to km/h by multiplying by 60. Multiply by 3.6.
How speed, distance and time are examined
Speed, distance and time questions appear at both tiers for Edexcel GCSE (1MA1) and International GCSE (4MA1) students, both as calculations and through distance–time graphs. Questions ask you to:
- work out a speed, distance or time, including times in minutes
- find the average speed for a journey with several parts
- read and interpret a distance–time graph
- convert between m/s and km/h
Practise with the compound measures worksheet, which has answers, or use the proportion revision engine.
Speed is one of the compound measures. Gradients of curved graphs are covered in rates of change.
Frequently asked questions
How is speed calculated?
Speed = distance ÷ time.
How do you find average speed?
Divide the total distance by the total time, including any stops.
How do you convert m/s to km/h?
Multiply by 3.6.