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.
Before radar guns and GPS, early attempts to measure speed were remarkably physical: 19th-century sailors measured a ship's speed using a “log line,” a rope with evenly spaced knots that was thrown overboard and let out for a fixed time, and the number of knots that passed through a sailor's hands gave the ship's speed – which is exactly why we still measure a ship's or aircraft's speed in “knots” today. Modern speed measurement got dramatically more precise with the invention of radar (RAdio Detection And Ranging) in the 1930s and 40s, which police still use to catch speeding drivers by bouncing radio waves off a moving vehicle and measuring the change in frequency of the reflected signal. At the extreme end of the scale, light itself travels at a fixed speed of about 300,000 km/s in a vacuum – the fastest speed anything in the universe can ever reach, according to Einstein's theory of relativity.
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
Speed = 240 ÷ 3 = 80 km/h.
Distance = 15 × 2.5 = 37.5 km.
Time = 400 ÷ 8 = 50 seconds.
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).