Step-by-step worked examples and graded practice questions on speed — unit conversions, average speed over multi-stage journeys, and distance-time graphs.
📚 Foundation & Higher✅ 15 Practice Questions🔍 Full Worked Examples⚠️ Common Mistakes
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Speed = distance ÷ time. Using the formula triangle: Distance = Speed × Time, with distance at the top, and speed and time on the bottom.
Cover the letter you want to find — whatever's left shows the calculation to use.
Converting units of speed
Speed is often needed in different units. The most common conversion is between km/h and m/s: multiplying by 1000 (m in a km) and dividing by 3600 (seconds in an hour) is the same as dividing by 3.6.
Worked Example 1
Convert 72km/h to m/s.
1
Convert km to m: 72km = 72,000m
2
Convert hours to seconds: 1 hour = 3600 seconds
3
Divide: 72,000 ÷ 3600 = 20
Answer20m/s
As a shortcut: divide km/h by 3.6 to get m/s, or multiply m/s by 3.6 to get km/h.
Average speed over a journey
Worked Example 2
A car travels 60km at 30km/h, then a further 90km at 45km/h. Find the average speed for the whole journey.
1
Find the time for the first stage: 60 ÷ 30 = 2 hours
2
Find the time for the second stage: 90 ÷ 45 = 2 hours
3
Find the total distance and total time: 60 + 90 = 150km, 2 + 2 = 4 hours
4
Average speed = total distance ÷ total time: 150 ÷ 4 = 37.5
Answer37.5km/h
Average speed is never the simple average of the individual speeds — it must always be calculated from the total distance and total time.
Reading speed from a distance-time graph
On a distance-time graph, speed is represented by the gradient of the line. A steeper line means a faster speed; a horizontal line means the object has stopped.
Both runners start together, but Runner B's line rises more steeply — covering more distance in the same time means a higher speed.
Worked Example 3
On a distance-time graph, a straight line goes from (0,0) to (5,100), where the x-axis shows time in seconds and the y-axis shows distance in metres. Find the speed represented by the line.
1
Speed is the gradient: change in distance ÷ change in time
2
Substitute the coordinates: 100 ÷ 5 = 20
Answer20m/s
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1Convert 10m/s to km/h.Foundation
Q2A car travels 180km in 3 hours. Find its average speed, in km/h.Foundation
Q3A runner covers 100m in 20 seconds. Find their speed, in m/s.Foundation
Q4A train travels at 90km/h for 2 hours. Find the distance travelled.Foundation
Q5Convert 54km/h to m/s.Foundation
Higher (Grade 5–7)
Q6A cyclist rides 12km in 30 minutes. Find their average speed, in km/h.Higher
Q7A car travels 240 miles in 4 hours. Find its speed in mph, then convert this to miles per minute.Higher
Q8A plane flies at 800km/h. How far does it travel in 45 minutes?Higher
Q9A jogger runs 400m in 100 seconds, then walks a further 200m in 200 seconds. Find their average speed for the entire 600m, in m/s.Higher
Q10Convert a speed of 25m/s into km/h.Higher
Higher — Hard (Grade 8–9)
Q11A car travels the first half of a 240km journey at 40km/h, and the second half at 60km/h. Find the average speed for the whole journey, in km/h.Grade 8–9
Q12A car travels for 2 hours at 45km/h, then for 3 hours at 65km/h. Find the average speed for the entire journey, in km/h.Grade 8–9
Q13On a distance-time graph, a straight line goes from (0,0) to (5,100), where x is time in seconds and y is distance in metres. Find the speed represented by the line, in m/s.Grade 8–9
Q14Two towns are 210km apart. A car sets off from each town at the same time, travelling towards each other — one at 50km/h and the other at 55km/h. Find how long it takes for them to meet, in hours.Grade 8–9
Q15A cyclist travels 6km at 20km/h, then stops for 12 minutes, then travels a further 9km at 18km/h. Find the average speed for the entire journey, including the stop, in km/h.Grade 8–9
Answers
Foundation (Q1–Q5)
Q136km/h(10 × 3.6)
Q260km/h
Q35m/s
Q4180km
Q515m/s(54 ÷ 3.6)
Higher (Q6–Q10)
Q624km/h(30 min = 0.5h, 12 ÷ 0.5)
Q760mph = 1 mile per minute(60 ÷ 60)
Q8600km(45 min = 0.75h, 800 × 0.75)
Q92m/s(600m ÷ 300s)
Q1090km/h(25 × 3.6)
Higher — Hard (Q11–Q15)
Q1148km/h(120km at 40km/h = 3h, 120km at 60km/h = 2h, 240 ÷ 5)
Using minutes instead of hours in a km/h or mph calculation
A time given in minutes must be converted to hours (divide by 60) before it can be used in a speed formula measured in km/h or mph.
Common Mistake 2
Averaging speeds instead of using total distance ÷ total time
Adding two speeds and dividing by 2 only works if the time spent at each speed is equal — the safe method is always total distance ÷ total time.
Common Mistake 3
Forgetting to include stopped time in average speed
If a journey includes a stop, that time still counts towards the total time for the average speed calculation, even though no distance is covered.
Common Mistake 4
Misreading the gradient on a distance-time graph
The gradient is change in distance ÷ change in time — reading the axes the wrong way round gives the reciprocal of the actual speed.
Exam tips
💡 Exam Tip 1
Convert units before you calculate, not after
Sort out minutes-to-hours or km-to-m conversions as your very first step — trying to convert a final answer is much more error-prone.
💡 Exam Tip 2
Set out multi-stage journeys in a table
List each stage's distance and time in a small table before totalling — this makes it much harder to accidentally mix up which time belongs to which distance.
💡 Exam Tip 3
Remember the ÷3.6 shortcut
Dividing by 3.6 converts km/h to m/s, and multiplying by 3.6 converts m/s to km/h — memorising this one shortcut saves time on nearly every speed conversion question.
💡 Exam Tip 4
For "meeting" problems, add the speeds
When two objects move towards each other, their speeds combine — use the sum of both speeds as a single "closing speed" to find the time until they meet.
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