Formula sheet
Average speed
This relationship is provided on the exam formula sheet. What you must supply is the thinking: add up every part of the journey to get the total distance and the total time before dividing, and make sure the distance and time units match the speed unit you want (for km/h, use km and hours).
What the symbols mean
- Average speed the single steady speed that would cover the whole journey in the same time (e.g. km/h or m/s)
- Total distance the sum of all distances travelled over the whole journey (e.g. km or m)
- Total time the sum of all time taken, in units that match the speed (e.g. hours for km/h, seconds for m/s)
Given in the exam, or memorise?
This relationship is provided on the exam formula sheet. What you must supply is the thinking: add up every part of the journey to get the total distance and the total time before dividing, and make sure the distance and time units match the speed unit you want (for km/h, use km and hours).
Why it works
Average speed answers a simple question, if the whole trip were done at one unchanging speed, what would it be?
- Speed is distance covered per unit of time.
- For a journey in several parts, add all the distances and add all the times.
- Dividing the total distance by the total time spreads the whole trip evenly, giving the average speed.
Worked example 1
A car travels 150 km in 2 hours, then a further 90 km in 1 hour. Find its average speed for the whole journey.
- Total distance = 150 + 90 = 240 km.
- Total time = 2 + 1 = 3 hours.
- Average speed = Total distance / Total time = 240 / 3
- = 80
Worked example 2
A van covers 60 km in the first hour, then 30 km in the next 30 minutes. Find its average speed in km/h.
- Total distance = 60 + 30 = 90 km.
- Convert 30 minutes to hours: 30 ÷ 60 = 0.5 h.
- Total time = 1 + 0.5 = 1.5 hours.
- Average speed = 90 / 1.5 = 60
Where students go wrong
- Averaging the two speeds instead of dividing total distance by total time, e.g. taking (75 + 60)/2. Average speed is not the mean of the speeds.
- Mixing units, leaving time in minutes while the answer must be in km/h. Convert minutes to hours (÷ 60) first.
- Using only part of the journey's distance or time instead of the totals.
- Writing a bare number without the unit, always state km/h or m/s in the answer.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Why can't I just average the speeds of each part?
Because the parts usually take different amounts of time. Speed must be weighted by how long each leg lasts, and dividing total distance by total time does that automatically.
Averaging the speeds only gives the same answer in the special case where each leg takes exactly the same time.
Do I use minutes or hours for the time?
Match the unit you want in the answer. For an answer in km/h, the time must be in hours, so convert any minutes by dividing by 60 (30 minutes = 0.5 h).
For m/s, use seconds. Keeping distance and time in matching units is the most common place marks are lost.
Is average speed the same as average velocity?
Not always. Average speed uses the total distance actually travelled, so it is always positive.
Average velocity uses displacement, the straight-line change in position and direction, which can be smaller or even zero for a round trip. Questions on this formula ask for average speed using total distance.