Speed - Distance, Time and Rate of Travel
Speed tells us how fast an object is moving. It connects distance and time in one of the most important and widely used formulas in mathematics and science.
The Speed Formula
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
A useful memory aid: arrange the three quantities in a triangle with D on top, S and T on the bottom.
Units of Speed
| Unit | Symbol | Used for | Conversion |
|---|---|---|---|
| Metres per second | m/s | Science, sprinting | 1 m/s = 3.6 km/h |
| Kilometres per hour | km/h | Road speeds, weather | 1 km/h ≈ 0.278 m/s |
| Miles per hour | mph | UK and US road signs | 1 mph ≈ 1.609 km/h |
Average Speed
Average speed = total distance ÷ total time. If a journey is split into stages, add all distances and divide by the total time – do not average the speeds directly.
Worked Examples
A car travels 240 km in 3 hours. Find its average speed in km/h.
Speed = 240 ÷ 3 = 80 km/h.
A cyclist travels at 15 km/h for 2.5 hours. How far do they travel?
Distance = 15 × 2.5 = 37.5 km.
A runner covers 400 m at a speed of 8 m/s. How long does it take?
Time = 400 ÷ 8 = 50 seconds.
Convert 90 km/h to m/s.
90 km/h = 90 × 1,000 m ÷ 3,600 s = 90,000 ÷ 3,600 = 25 m/s.
Key Takeaways
- Speed = Distance ÷ Time. Units must be consistent.
- To convert km/h to m/s: divide by 3.6. To convert m/s to km/h: multiply by 3.6.
- Average speed = total distance ÷ total time (not the average of individual speeds).
Practice Questions
- A train travels 360 km in 4 hours. Find its average speed.
- A bus travels at 50 km/h for 1.5 hours. How far does it travel?
- A plane flies 1,800 km at 600 km/h. How long is the flight?
- Convert 72 km/h to m/s.
- A sprinter runs 100 m in 10 seconds. What is their speed in m/s and in km/h?