S3.7.1 Chapter 1

Speed

How fast do I walk? Can I measure it at home?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

A Measure a distance, time your walk, then divide the distance by the time.
You picked A. Read on. At the end, the chapter comes back to your guess.
B You need a machine, so you cannot measure it at home.
You picked B. Read on. At the end, the chapter comes back to your guess.
C Speed is just how long the walk takes.
You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

Calculate speed from distance and time
Measure your walking speed in metres per second

Amina and her brother go to the well. Amina walks and her brother runs. He gets there first, so he was faster. But how much faster? To say, we need a number.

The speed of a thing tells how far it goes in one second. We measure speed in metres per second. We write m/s.

A speed of 2 m/s means 2 metres every second. A person walking goes about 1 to 1.5 metres each second.

A walker at 2 m/s is 2 metres farther on every second. After 4 seconds she has gone 8 metres.

Draw it first

Draw a walk and its speed

1 Draw a track. Mark 0, 6, 12 and 18 metres. Draw the walker at the start.
2 Move the walker to the end. Write the distance and the time: 18 m in 12 s.
3 Divide the distance by the time. 18 ÷ 12 = 1.5. The speed is 1.5 m/s.

To find a speed you need two measurements. One is the distance, how far the thing went, in metres. The other is the time it took, in seconds.

Then share the distance out among the seconds. That gives the metres for each second.

See it three ways

As a picture

In words

A walker goes 1.5 metres every second. In 2 seconds she goes 3 metres. The distance grows by the same amount each second.

In symbols

speed = distance ÷ time. 18 m ÷ 12 s = 1.5 m/s.

The runner in the next worked example. Read the distance and the time from the picture.

Worked example

Kofi runs 40 m in 10 s. What is his speed?

Speed = distance ÷ time.
The distance is 40 m. The time is 10 s.
Speed = 40 ÷ 10 = 4 m/s.

Answer: 4 m/s

You can turn the rule around. If you know the speed and the time, then distance = speed × time. If you know the distance and the speed, then time = distance ÷ speed.

A real walk is never perfectly even. You slow down on a hill and speed up on flat ground. So the number you find is the average speed: the total distance divided by the total time.

A slow part and a fast part. The average speed uses the whole distance and the whole time.

Try it

Measure your walking speed

You need: a string or stick to measure 12 metres, two stones to mark the start and the end, a clock, or a friend who counts seconds ("one thousand and one, one thousand and two"), paper and a pencil.

Be safe: Walk on flat ground, well away from roads and holes. Do not run.

Mark a start and an end 12 metres apart on flat ground. Put a stone at each.
Stand at the start. Your friend says "go" and starts counting seconds.
Walk at your normal pace to the end stone. Do not run.
Write the time in seconds. Do the walk three times.
For each walk, divide 12 by the time. Write the speed in metres per second.

What you will see: Your three speeds will be close, but not the same. Ours are 1.2, 1.2, 1 m/s. A walk usually comes out between 1 and 1.5 m/s. Your numbers will differ from ours, and that is fine.

If you cannot try it, this is what happens.

Ravi walks 60 m in 60 s. Mei runs 30 m in 10 s. Ravi goes farther, but Mei is faster.

A wrong idea many people have

The one that goes the farthest is the fastest.

Why it feels right: Going a long way looks like hard work, so it seems to need more speed.

The test that breaks it: Ravi walks 60 m in 60 s. Mei runs 30 m in 10 s. Ravi went farther. Divide each: Ravi 1 m/s, Mei 3 m/s. Mei is faster.

What is true: Speed needs the distance and the time together. A short trip in a short time can be faster than a long, slow trip.

Key words

speed: how far a thing goes in one second.
metres per second: the unit of speed. We write m/s.
distance: how far a thing goes, measured in metres.
average speed: the total distance divided by the total time.

Back to your guess

The answer is A: Measure a distance, time your walk, then divide the distance by the time.

Measure a distance, time your walk, then divide the distance by the time. A string and a clock are enough. Speed needs both numbers, not only the time.

Keep it

Copy this into your exercise book.

Speed is how far a thing goes in one second. Speed = distance ÷ time. We write it in metres per second, m/s. Distance = speed × time.

Draw: A track marked 0 and 12 metres. Under it write 12 m ÷ 10 s = 1.2 m/s.