☰ Year plan · Mathematics

Conversion factors and changing units

Week 21 · Conversion factors for lengths, masses, capacities and speeds · 3 lessons
3

Converting speeds and other rates

Discover Mathematics P6: Term 2, Unit 10, Lessons 4–6
GoalConvert speeds between km/h and m/s and compare converted measures.
New words
speed · a rate: the distance travelled in one unit of timekm/h · kilometres per hourm/s · metres per second
Explanation

A speed has two units, one for distance and one for time, so we use two conversion factors. 1 km = 1,000 m and 1 h = 3,600 s (60 × 60). To change km/h into m/s, multiply by 1,000 m / 1 km and by 1 h / 3,600 s. In short: multiply by 1,000 and divide by 3,600. So 72 km/h = 72 × 1,000 ÷ 3,600 = 20 m/s. To go back from m/s to km/h, do the opposite: multiply by 3,600 and divide by 1,000. 15 m/s = 15 × 3,600 ÷ 1,000 = 54 km/h. To compare two speeds, first write them in the same unit.

ƒFormula
km/h → m/s: × 1,000 ÷ 3,600 m/s → km/h: × 3,600 ÷ 1,000
Worked examples
km/h3672108
m/s102030
A train runs at 72 km/h. In one hour it goes 72,000 m, and an hour has 3,600 s. 72,000 ÷ 3,600 = 20, so it goes 20 m every second: 72 km/h = 20 m/s.
A runner does 8 m/s. In km/h that is 8 × 3,600 ÷ 1,000 = 28.8 km/h. A cyclist rides at 25 km/h. Which is faster? 28.8 is more than 25, so the runner is faster.
Heights too. A palm tree is 8.5 m tall and a pole is 900 cm tall. Write both in metres: 900 cm = 9 m. The pole is taller by 9 − 8.5 = 0.5 m.
Class activity

Speed detective. Ask a grown-up what speed the family car shows on the road in km/h. Change it to m/s. How many metres does the car go in one second?

Practice
1
Change 36 km/h into m/s.
2
Change 25 m/s into km/h.
3
A bus goes 108 km/h. How many metres per second is that?
4
Which is faster, 20 m/s or 60 km/h?
5
A boy is 1.6 m tall and his sister is 150 cm tall. Who is taller and by how many centimetres?