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
  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • 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 track marked in metres with the numbers 0, 2, 4, 6 and 8 and the label metres. A walker is shown as a dot at 0 s, 1 s, 2 s, 3 s and 4 s, each dot 2 metres farther on than the one before, with arrows between them. The label above says every second: 2 m. Labels: every second: 2 m, 0 s, 1 s, 2 s, 3 s, 4 s, 0, 2, 4, 6, 8, metres.0 s1 s2 s3 s4 s02468metresevery second: 2 m
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. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresstart

    1 Draw a track. Mark 0, 6, 12 and 18 metres. Draw the walker at the start.

  2. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresend18 m in 12 s

    2 Move the walker to the end. Write the distance and the time: 18 m in 12 s.

  3. A straight track with marks at 0, 6, 12 and 18, with the label metres. In the first picture a person stands at 0, labelled start. In the second the person is at 18, labelled end, and an arrow runs along the track, labelled 18 m in 12 s. In the third the speed is written: speed = 18 m ÷ 12 s = 1.5 m/s.061218metresend18 m in 12 sspeed = 18 m ÷ 12 s = 1.5 m/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

A table with two columns, time in seconds and distance in metres. At 0 seconds the distance is 0. Then 2 and 3, 4 and 6, 6 and 9, 8 and 12.secondsmetres00234669812

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.

A track marked 0, 10, 20, 30 and 40 with the label metres. The label start is at 0 and the label end is above a runner at 40. An arrow runs along the track, labelled 40 m in 10 s. Labels: start, end, 0, 10, 20, 30, 40, metres, 40 m in 10 s.010203040metresstartend40 m in 10 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?

  1. Speed = distance ÷ time.
  2. The distance is 40 m. The time is 10 s.
  3. 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 track marked 0, 30 and 60 with the label metres. The first part, labelled walk, is 30 m, 30 s. The second part, labelled run, is 30 m, 10 s. Below is written 60 m ÷ 40 s = 1.5 m/s. Labels: walk, run, 0, 30, 60, metres, 30 m, 30 s, 30 m, 10 s, 60 m ÷ 40 s = 1.5 m/s.03060metreswalkrun30 m, 30 s30 m, 10 s60 m ÷ 40 s = 1.5 m/s
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.

  1. Mark a start and an end 12 metres apart on flat ground. Put a stone at each.
  2. Stand at the start. Your friend says "go" and starts counting seconds.
  3. Walk at your normal pace to the end stone. Do not run.
  4. Write the time in seconds. Do the walk three times.
  5. 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.
A table of one learner's walks of 12 metres. The head row says walk, seconds and m/s. Walk 1: 10 seconds, 1.2 m/s. Walk 2: 10 seconds, 1.2 m/s. Walk 3: 12 seconds, 1 m/s.walksecondsm/s1101.22101.23121
A bar chart called speed (m/s). The bar for Ravi reaches 1. The bar for Mei reaches 3. The scale goes from 0 to 4 in steps of 1. Labels: speed (m/s), Ravi, Mei, 0, 1, 2, 3, 4.01234RaviMeispeed (m/s)
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.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Mei walks 36 m in 30 s. What is her speed?

    See the answer

    1.2 m/s

    Speed = distance ÷ time = 36 ÷ 30 = 1.2 m/s.

  2. A cyclist rides at 4 m/s for 10 s. How far does she go?

    Tap your answer.
    1. Not this one. You divided the time by the speed. To find a distance, multiply the speed by the time. Go to S3.7.1. Try another.

    2. Yes, that is right. Distance = speed × time = 4 × 10 = 40 m.

    3. Not this one. You added the speed and the time. A speed of 4 m/s means 4 metres every second, so multiply by the seconds. Go to S3.7.1. Try another.

    See the answer

    40 m

    Distance = speed × time = 4 × 10 = 40 m.

    • If you chose A: You divided the time by the speed. To find a distance, multiply the speed by the time. Go to S3.7.1.
    • If you chose C: You added the speed and the time. A speed of 4 m/s means 4 metres every second, so multiply by the seconds. Go to S3.7.1.
  3. Joseph walks at 2 m/s. How long does he take to walk 50 m?

    Tap your answer.
    1. Not this one. You divided the speed by the distance, upside down. Time = distance ÷ speed. Go to S3.7.1. Try another.

    2. Not this one. You multiplied the distance by the speed. That gives a distance, not a time. Divide the distance by the speed. Go to S3.7.1. Try another.

    3. Yes, that is right. Time = distance ÷ speed = 50 ÷ 2 = 25 s.

    4. Not this one. You added the distance and the speed. They are different kinds of number, so they cannot be added. Divide instead. Go to S3.7.1. Try another.

    See the answer

    25 s

    Time = distance ÷ speed = 50 ÷ 2 = 25 s.

    • If you chose A: You divided the speed by the distance, upside down. Time = distance ÷ speed. Go to S3.7.1.
    • If you chose B: You multiplied the distance by the speed. That gives a distance, not a time. Divide the distance by the speed. Go to S3.7.1.
    • If you chose D: You added the distance and the speed. They are different kinds of number, so they cannot be added. Divide instead. Go to S3.7.1.
  4. Ana walks 20 m in 10 s. Tariq walks 30 m in 20 s. Who is faster?

    Tap your answer.
    1. Yes, that is right. Ana: 20 ÷ 10 = 2 m/s. Tariq: 30 ÷ 20 = 1.5 m/s. Ana has the bigger number.

    2. Not this one. Tariq went farther, but he also took longer. Divide each distance by its time and compare. Go to S3.7.1. Try another.

    3. Not this one. Work out each speed. Distance ÷ time is not the same for both. Go to S3.7.1. Try another.

    See the answer

    Ana

    Ana: 20 ÷ 10 = 2 m/s. Tariq: 30 ÷ 20 = 1.5 m/s. Ana has the bigger number.

    • If you chose B: Tariq went farther, but he also took longer. Divide each distance by its time and compare. Go to S3.7.1.
    • If you chose C: Work out each speed. Distance ÷ time is not the same for both. Go to S3.7.1.
  5. Kofi walks 40 m in 40 s. Then he runs 40 m in 10 s. What is his average speed for the whole trip?

    Tap your answer.
    1. Not this one. You added the two speeds and halved them. Use the total distance and the total time instead. Go to S3.7.1. Try another.

    2. Yes, that is right. Total distance = 40 + 40 = 80 m. Total time = 40 + 10 = 50 s. 80 ÷ 50 = 1.6 m/s.

    3. Not this one. That is only the running part. Average speed uses the whole trip. Go to S3.7.1. Try another.

    See the answer

    1.6 m/s

    Total distance = 40 + 40 = 80 m. Total time = 40 + 10 = 50 s. 80 ÷ 50 = 1.6 m/s.

    • If you chose A: You added the two speeds and halved them. Use the total distance and the total time instead. Go to S3.7.1.
    • If you chose C: That is only the running part. Average speed uses the whole trip. Go to S3.7.1.
  6. To find your walking speed at home, which two measurements do you need?

    Tap your answer.
    1. Not this one. The time alone cannot tell the speed. A short walk takes little time even when it is slow. Go to S3.7.1. Try another.

    2. Not this one. The distance alone cannot tell the speed. A long walk is slow if it takes a long time. Go to S3.7.1. Try another.

    3. Yes, that is right. Speed is distance divided by time, so you need both. Mark a distance with stones, time the walk, then divide. Do it three times, because a walk is never perfectly even.

    See the answer

    The distance you walk and the time it takes.

    Speed is distance divided by time, so you need both. Mark a distance with stones, time the walk, then divide. Do it three times, because a walk is never perfectly even.

    • If you chose A: The time alone cannot tell the speed. A short walk takes little time even when it is slow. Go to S3.7.1.
    • If you chose B: The distance alone cannot tell the speed. A long walk is slow if it takes a long time. Go to S3.7.1.

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.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (881 KB). It opens on any phone.