Speed and average rates

A speed is distance per unit time

A 150 km journey completed in 2.5 h has average speed 150/2.5 = 60 km/h. Distance = speed × time and time = distance ÷ speed when the chosen speed describes that whole interval.

Average speed need not be the instantaneous speed at any particular moment. A stop contributes time even when no distance is covered, if the question includes that stop in the journey.

Convert the complete rate

72 km/h = 72 × 1000÷3600 = 20 m/s. One hour contains 3600 seconds, not 60 seconds. In reverse, 5 m/s = 5 × 3600÷1000 = 18 km/h.

For a rate in metres per minute, divide the kilometre-per-hour value by 60 and multiply by 1000. Keep the unit labels through the calculation rather than memorising an unlabelled conversion factor.

Combine distances and times

A cyclist travels 30 km at 10 km/h, then 30 km at 15 km/h. Times are 3 h and 2 h, total 5 h. Average speed is 60/5 = 12 km/h, not (10 + 15)/2 = 12.5 km/h. Equal distances do not mean equal times.

If the cyclist spends equal times at the two speeds, the simple average does work: two hours at each gives distances 20 km and 30 km, so 50/4 = 12.5 km/h. Derive the average from totals first.

Check your understanding 1 Does the stop count?

A train travels 80 km in 1 hour, stops for 20 minutes, then travels another 40 km in 40 minutes. Find its average speed for the full elapsed journey.

Your answer or drawing on paper

Show answer

Total distance is 120 km. Total time is 2 h, including the stop. Average speed is 60 km/h. Excluding the stop would answer a different question.

Check a units claim

A runner moves at 4 m/s for 5 minutes. Find the modelled distance in kilometres.