Time, Distance, and Speed
3.0 Measurements · 3.5 Time, Distance, and Speed
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.5 Time, Distance, and Speed (8 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Identify and convert units of time and distance
- Identify speed as distance covered per unit time
- Work out speed in km/h and m/s, and convert between them
- Reflect on the use of time, distance and speed in real life, including road safety
Time, Distance and Speed
Speed connects how far something goes with how long it takes. The three quantities are linked by one rule, and knowing any two gives the third.
a) Units of time and distance
Time: 60 seconds make a minute, 60 minutes make an hour, 24 hours make a day.
Distance: 1 000 metres make a kilometre, 100 centimetres make a metre.
Convert to the units you want before calculating. Mixing minutes and hours in one sum is the usual source of wrong answers.
Note that 2 hours 30 minutes is 2.5 hours, not 2.3 hours. Minutes are sixtieths, not hundredths.
b) The rule
Speed is the distance covered in one unit of time.
The rule rearranges two ways. Distance = speed × time, and time = distance ÷ speed.
Cover the quantity you want in the triangle formula and read off what is left.
c) Units of speed
Speed is always a distance unit over a time unit: km/h, m/s, or km/min.
The units tell you what the number means. A speed of 75 means nothing on its own; 75 km/h means 75 kilometres are covered each hour.
d) Converting km/h to m/s
To go from km/h to m/s, multiply by 1 000 and divide by 3 600. That is the same as dividing by 3.6.
To go the other way, multiply by 3.6.
A check: the numbers come out smaller in m/s. So 72 km/h becomes 20 m/s.
e) Reading a journey graph
Distance is plotted up the page and time across.
A steep line means fast travelling. A gentle line means slow.
A flat line means the distance is not changing, so the traveller has stopped.
Here the journey covers 150 km in the first two hours, rests during the third, then continues.
Speed on any section is the distance covered divided by the time taken for that section.
f) Road safety
Higher speed means less time to react and a longer distance to stop.
Doubling speed does not double stopping distance. It makes it roughly four times longer, because braking distance depends on speed squared.
This is why speed limits are lower near schools and markets.
g) Where this is used
A driver estimating arrival time. A bus company setting a timetable. An athlete tracking pace. A traffic officer judging whether a limit was exceeded.
Words to know
- Speed — the distance covered per unit of time, calculated as distance ÷ time.
- km/h — kilometres per hour, a common unit of speed for road travel.
- m/s — metres per second, a common unit of speed for shorter distances or scientific contexts.
- Speed limiter — a device capping a vehicle's maximum speed, used for road safety.
:::checkpoint Check yourself
- A car covers 180 km in 3 hours. Find its speed.
- Convert 90 km/h into m/s.
- What does a flat section on a distance-time graph mean?
- How long does a 240 km journey take at 60 km/h? :::
Bridge to practice
Try the exercises below — on time and distance conversion, and calculating and converting speed.