Speed, distance, and time
Use one core relationship and careful unit conversion to solve common motion problems.
The core relationship#
speed = distance ÷ time. Rearranging gives distance = speed × time and time = distance ÷ speed.
If a vehicle travels 180 kilometres in 3 hours, its average speed is 60 kilometres per hour.
Compatible units#
Match units before calculating. To convert kilometres per hour to metres per second, multiply by 5/18. To reverse the conversion, multiply by 18/5.
Relative speed#
When two objects move toward each other, the distance between them closes at the sum of their speeds. When they move in the same direction, the faster object gains at the difference between their speeds.
Average speed#
Average speed is not usually the simple average of two speeds. It equals total distance divided by total time.
If a traveller covers 60 km at 30 km/h and another 60 km at 60 km/h, total time is 2 + 1 = 3 hours. Average speed is 120 ÷ 3 = 40 km/h, not 45.
Stops and delays#
Include stopped time when the question asks for overall average speed. Exclude it only when the wording asks for speed while moving.
Common mistakes#
Avoid mixing minutes with hours or metres with kilometres. Check whether the problem describes actual speed, average speed, or relative speed.
Reasonableness#
For a journey with positive speeds, the overall average should lie between the slowest and fastest segment speeds. A value outside that range indicates a setup or unit error.
Key points
- Speed equals distance divided by time.
- Convert all quantities to compatible units before calculation.
- Relative speeds add for opposite directions and subtract for the same direction.
- Average speed is total distance divided by total time.