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Time, Distance and Speed

Measurements · Time, Distance and Speed

Syllabus tag: Kenya CBC | Grade 9 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.4 Time, Distance and Speed (10 Lessons)

Lesson objectives

By the end of this sub-strand, you should be able to:

  • Work out speed in kilometres per hour and metres per second in real-life situations.
  • Convert between the two speed units confidently.
  • Calculate average speed for journeys made in stages.
  • Solve problems involving velocity, acceleration and relative motion.

Time, Distance and Speed

Every journey involves three things: how far, how long, and how fast. If you know any two of them, you can work out the third.

This topic also takes you around the globe. The reason Nairobi and Lagos read different clock times is a distance problem too.

a) Speed

Speed tells you how much distance is covered in each unit of time.

Working out speed Working out speed speed = distance / time write down the rule speed = 180 km / 3 h put in what you know speed = 60 km/h divide

Always write the unit. A speed of 60 means nothing on its own. 60 km/h and 60 m/s are very different things.

b) Changing between km/h and m/s

Questions often mix the two units. Change them before you calculate, never after.

Changing km/h into m/s Changing km/h into m/s 72 km/h = 72 000 m in 1 hour 1 km is 1000 m 72 km/h = 72 000 m in 3600 s 1 hour is 3600 s 72 km/h = 72 000 / 3600 divide 72 km/h = 20 m/s the answer

There is a shortcut once you understand the working above. To go from km/h to m/s, divide by 3.6. To go the other way, multiply by 3.6.

c) Average speed

A vehicle rarely holds one speed. It slows for bumps, stops for passengers, then speeds up again.

A matatu journey A matatu journey 0 1 2 3 4 5 0 30 60 90 120 time in hours distance in km

Read the graph carefully. A steep part means fast. A flat part means the vehicle is stopped, because time passes but distance does not change.

The average speed rule The average speed rule average speed = total distance total time
Average speed for the whole trip Average speed for the whole trip average = 120 km / 5 h use the totals, not each leg average = 24 km/h divide

Watch the trap here. Average speed is total distance divided by total time. It is not the average of the separate speeds. Those two give different answers.

d) Velocity and acceleration

Velocity is speed in a stated direction. 60 km/h is a speed. 60 km/h due north is a velocity.

Acceleration is how quickly the velocity changes.

The acceleration rule The acceleration rule acceleration = change in speed time taken
Working out acceleration Working out acceleration acceleration = (20 − 8) / 4 8 m/s to 20 m/s in 4 s acceleration = 3 m/s² divide

The unit looks strange at first. It is metres per second, per second, written m/s². It means the speed grows by 3 m/s during every second that passes.

If a vehicle is slowing down, the acceleration comes out negative.

e) Longitudes

Longitudes are the lines running from the North Pole to the South Pole. They tell you how far east or west a place is.

Longitudes run from pole to pole Longitudes run from pole to pole equator 0° 45°E 0° is the Greenwich meridian

The line through Greenwich in London is 0°. Every other longitude is measured east or west from it, up to 180°.

f) Local time from longitude

The Earth turns once, all 360°, in 24 hours. Divide one by the other and you get the rule that solves every question in this section.

The Earth turns 15° in one hour. So 1° takes 4 minutes.

Local time from longitude Local time from longitude difference = 45°E − 15°E the two longitudes difference = 30° subtract time gap = 30 × 4 min 1° is 4 minutes time gap = 2 hours 120 minutes

Now apply the direction. Places to the east see the sun earlier, so their clocks are ahead. Places to the west are behind.

So if it is 10:00 at 15°E, then at 45°E it is 12:00.

g) Where this is used

A matatu sacco works out average speeds to set realistic timetables. Airlines publish arrival times in local time. That is why a flight can seem to land before it took off. Athletics coaches at Iten use speed calculations in every training session.

Words to know

  • Speed -- the rate at which distance is covered, found by dividing distance by time.
  • Average speed -- total distance divided by total time for a complete journey.
  • Velocity -- speed together with a stated direction.
  • Acceleration -- the rate of change of velocity, measured in metres per second squared.
  • Relative speed -- the rate at which the gap between two moving objects changes.

:::checkpoint Check yourself

  1. A bus covers 240 km in 4 hours. What is its speed?
  2. Change 54 km/h into m/s.
  3. A car travels 60 km in 1 hour, rests for 1 hour, then travels 40 km in 1 hour. What is its average speed for the whole journey?
  4. If the local time at 20°E is 14:00, what is the local time at 50°E? :::

Bridge to practice

The exercises begin with direct substitution, move through unit conversion and time handling, and finish with average speed over stages and relative motion. When a journey has more than one stage, resist calculating anything until you have written down the distance and time for each stage separately; that single habit prevents the most common error in this topic.

Check yourselfPractise Time, Distance and Speed — 10 questions →Next in MathematicsTrigonometry →