A car travels 150 km in 2 hours. What is its average speed?
v = d ÷ t
Average speed is distance divided by time.
150 ÷ 2 = 75
I divide: 150 km spread over 2 hours makes 75 km each hour.
Result: The average speed is 75 km/h.
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Speed and compound quantities
Level 4 · Ages 13–15
Quick recall· Let's wake up what you already know before we start.
Recall: how many minutes are there in 1 h 30 min?
min
The whole lesson
Read it again any time, including while you work through the exercises.
A car travels 150 km in 2 hours. Is it fast? To answer, we invent a new quantity, built from two others: speed. It is a compound quantity, because it combines a distance and a duration.
Average speed is computed like this: v = d ÷ t, the distance divided by the time. Here, 150 ÷ 2 = 75: the car travels on average at 75 kilometres per hour, written 75 km/h. The unit itself tells the story of the computation: kilometres divided by hours!
This magic formula flips around every way. You know the speed and the time? The distance is d = v × t. You know the distance and the speed? The time is t = d ÷ v. A d, v, t triangle to know by heart.
Watch out for the unit trap: if the speed is in km/h, the time must be in hours! For a 30 minute trip, convert first: 30 min = 0.5 h. And to go from km/h to m/s, remember that 1 km = 1000 m and 1 h = 3600 s: we divide by 3.6.
Speed is only the beginning: you will soon meet other compound quantities, like the flow rate of a tap (litres per minute) or density (grams per cubic centimetre). The principle stays the same: two quantities combined into one.
The worked example, step by step
Convert 90 km/h to metres per second.
90 km = 90000 m
I convert the distance: 90 km is 90000 m.
1 h = 3600 s
I convert the time: 1 hour is 60 × 60 = 3600 seconds.
90000 ÷ 3600 = 25
I divide: 90000 m covered in 3600 s makes 25 m every second.
Result: 90 km/h = 25 m/s