Chapter 2 of 8

All 8 chapters
  1. 1Speed, readunderstood
  2. 2Distance and time graphs, readunderstood
  3. 3Balanced and unbalanced forces, readunderstood
  4. 4Mass and weight, readunderstood
  5. 5Stretching and springs, readunderstood
  6. 6Levers and turning forces, readunderstood
  7. 7Pressure, readunderstood
  8. 8Pressure in water and air, readunderstood

S3.7.2 Chapter 2

Distance and time graphs

Can a picture show how a whole journey went?

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

  • Draw a distance and time graph for a journey
  • Tell from a graph when an object is still, slow or fast

Mei walks to the market. She goes quickly, stops to talk, then walks on slowly. A list of numbers would be hard to read. A picture shows the whole journey at once.

A distance and time graph shows how far something is from home as time goes by. Time goes across. Distance goes up. Both start at 0.

Start with a table. It says where Mei was after each 10 seconds. Each row is one point on the line we draw.

A table with the columns seconds and metres from home. At 0 seconds, 0 metres. At 10 seconds, 20 metres. At 20 seconds, 40 metres. At 30 seconds, 40 metres. At 40 seconds, 40 metres. At 50 seconds, 45 metres. At 60 seconds, 50 metres.secondsmetres from home00102020403040404050456050
Mei is at 0 metres from home when she starts. Read down to see her move, stop and move on.

Draw it first

Draw the graph of a journey

  1. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060time in secondsdistance from home (m)

    1 Draw the axes. Mei walks 40 m in 20 s. Mark that point and join it to the start.

  2. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060time in secondsdistance from home (m)

    2 She stands still for 20 s. Her distance stays at 40 m, so draw a flat line.

  3. A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. First, a line climbs steeply from 0 to 40 metres in 20 seconds. Next it runs flat to 40 seconds. Last it climbs gently to 50 metres at 60 seconds. The three parts are labelled fast, still and slow. Labels: time in seconds, distance from home (m), fast, still, slow.01020304050600102030405060faststillslowtime in secondsdistance from home (m)

    3 Then she walks 10 m in 20 s. Draw a gentle line. Write fast, still and slow.

Read the graph from left to right, like a story. A flat line means the distance is not changing. The thing is still.

A line that climbs means the thing is moving away from home. The steeper the line, the faster the thing is going. A gentle climb is slow.

Two graphs with the same scale. Time in seconds runs across to 60. Distance from home goes up to 60 metres. Kofi: 60 m in 30 s, a steep line, labelled faster. Lucía: 60 m in 60 s, a gentle line, labelled slower. Labels: Kofi, Lucía, faster, slower, time in seconds, distance from home (m).Kofi: 60 m in 30 s01020304050600204060fastertime in secondsdistance from home (m)Lucía: 60 m in 60 s01020304050600204060slowertime in secondsdistance from home (m)
Both walkers go the same distance. Kofi takes less time, so his line is steeper.

You can find the speed of any part of a journey. Take the distance that part covers and divide it by the time it takes. This is the same rule as before.

See it three ways

As a picture

A table of Mei's journey with the columns part, seconds, metres and m/s. Part 1st: 20 seconds, 40 metres, 2 m/s. Part 2nd: 20 seconds, 0 metres, 0 m/s. Part 3rd: 20 seconds, 10 metres, 0.5 m/s.partsecondsmetresm/s1st204022nd20003rd20100.5

In words

The steep part has the biggest speed. The flat part has a speed of zero. The gentle part is in between.

In symbols

Fast part: 40 ÷ 20 = 2 m/s. Still part: 0 ÷ 20 = 0 m/s. Slow part: 10 ÷ 20 = 0.5 m/s.

A graph of the first part of Mei's journey. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs from 0 to 40 metres at 20 seconds, labelled first part. Labels: time in seconds, distance from home (m), first part.01020304050600102030405060first parttime in secondsdistance from home (m)
Read two numbers from this part: how far, and how long. Then divide.

Worked example

Use Mei's graph. What is her speed in the first part, from 0 s to 20 s?

  1. At 20 s the graph is at 40 m.
  2. The part starts at 0 s and ends at 20 s. It lasts 20 s.
  3. Speed = distance ÷ time = 40 ÷ 20 = 2 m/s.
  4. The line is steep, so this is the fast part.

Answer: 2 m/s

All the graphs here show distance from home. So a line that goes down means the walker is coming back towards home.

Try it

Draw the graph of your own walk

You need: five stones, a string and a stick to space them 3 metres apart, a clock, or a friend who counts seconds, paper with a ruler for the lines, and a pencil.

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

  1. Put the stones in a straight line, 3 metres apart. Stand at the first stone.
  2. Your friend says "go". Walk at your normal pace past all the stones.
  3. Your friend writes the second you reach each stone.
  4. On paper, draw time across and distance up. Both start at 0.
  5. Mark a point for each stone. Join the points with straight lines.

What you will see: The line is close to straight, with a few small bends. A walk is never perfectly even. A straight line means a steady speed. The dashed line shows the pattern.

If you cannot try it, this is what happens.
A graph of one learner's walk. Time in seconds runs across to 10, with 0, 2, 4, 6, 8, 10. Distance walked goes up to 12 metres, with 0, 3, 6, 9, 12. The points are 0 s and 0 m, 2 s and 3 m, 5 s and 6 m, 8 s and 9 m, 10 s and 12 m. A dashed straight line runs close to all the points. Labels: time in seconds, distance walked (m).0246810036912time in secondsdistance walked (m)

A wrong idea many people have

A line that goes up on the graph means the walker is going uphill.

Why it feels right: The line looks like a hill, so it is tempting to read it as a path.

The test that breaks it: Walk 10 steps on flat ground, then stand still for 10 seconds. Draw the graph. It climbs, then goes flat. The ground was flat the whole way.

What is true: The graph is not a picture of the path. Up means farther from home as time goes by. Flat means not moving.

Key words

distance and time graph
a graph with time across and distance from home up.
still
not moving. The graph line is flat.
steeper
climbing more quickly. A steeper line means a faster speed.

Back to your guess

The answer is A: A flat line on the graph means the walker is standing still.

A flat line means the distance is not changing, so the walker is standing still. The graph shows distance from home against time. It does not show the shape of the ground.

Check yourself

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

  1. Look at Ravi's graph. In which part is he standing still?

    A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs to 10 metres at 10 seconds, climbs more steeply to 50 metres at 30 seconds, then runs flat until 50 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Not this one. The line climbs here, so the distance is growing. He is moving. Look for the flat part. Go to S3.7.2. Try another.

    2. Yes, that is right. A flat line means the distance does not change. He is still from 30 s to 50 s.

    3. Not this one. The line climbs steeply here. A fast walk is not standing still. Look for the flat part. Go to S3.7.2. Try another.

    See the answer

    From 30 s to 50 s

    A flat line means the distance does not change. He is still from 30 s to 50 s.

    • If you chose A: The line climbs here, so the distance is growing. He is moving. Look for the flat part. Go to S3.7.2.
    • If you chose C: The line climbs steeply here. A fast walk is not standing still. Look for the flat part. Go to S3.7.2.

  2. Use the same graph. In which part does Ravi move fastest?

    A graph. Time in seconds runs across, with 0, 10, 20, 30, 40, 50, 60. Distance from home in metres goes up, with 0, 10, 20, 30, 40, 50, 60. A line climbs to 10 metres at 10 seconds, climbs more steeply to 50 metres at 30 seconds, then runs flat until 50 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Not this one. This part is flat, so he is not moving. The fastest part is the steepest. Go to S3.7.2. Try another.

    2. Not this one. The line climbs here, but not as steeply as later. Find the steepest part. Go to S3.7.2. Try another.

    3. Yes, that is right. The middle part is the steepest. He goes 40 m in 20 s, which is 2 m/s.

    See the answer

    From 10 s to 30 s

    The middle part is the steepest. He goes 40 m in 20 s, which is 2 m/s.

    • If you chose A: This part is flat, so he is not moving. The fastest part is the steepest. Go to S3.7.2.
    • If you chose B: The line climbs here, but not as steeply as later. Find the steepest part. Go to S3.7.2.

  3. Ana's graph shows her distance from home. What does she do between 30 s and 40 s?

    A graph of Ana's distance from home. Time in seconds runs across to 60, with 0, 10, 20, 30, 40, 50, 60. Distance from home goes up to 60 metres, with 0, 10, 20, 30, 40, 50, 60. The line climbs to 20 metres at 10 seconds, runs flat until 30 seconds, then goes down to 10 metres at 40 seconds. Labels: time in seconds, distance from home (m).01020304050600102030405060time in secondsdistance from home (m)
    Tap your answer.

    1. Yes, that is right. The line goes down, so her distance from home gets smaller.

    2. Not this one. Her distance from home gets smaller here, so she is coming closer. Check which way the line goes. Go to S3.7.2. Try another.

    3. Not this one. A still walker has a flat line. This line goes down. Go to S3.7.2. Try another.

    See the answer

    She walks back towards home.

    The line goes down, so her distance from home gets smaller.

    • If you chose B: Her distance from home gets smaller here, so she is coming closer. Check which way the line goes. Go to S3.7.2.
    • If you chose C: A still walker has a flat line. This line goes down. Go to S3.7.2.

  4. Mei is 40 m from home after 20 s. You draw her graph. Where do you mark this point?

    Tap your answer.

    1. Not this one. You swapped the two scales. On this graph time goes across and distance goes up, so start with the time. Go to S3.7.2. Try another.

    2. Yes, that is right. Time goes across and distance goes up. The point is 20 s across and 40 m up.

    3. Not this one. That puts the point at 0 seconds, on the up line. Go across to the time first, then up. Go to S3.7.2. Try another.

    See the answer

    Across to 20 on the time scale, then up to 40 on the distance scale

    Time goes across and distance goes up. The point is 20 s across and 40 m up.

    • If you chose A: You swapped the two scales. On this graph time goes across and distance goes up, so start with the time. Go to S3.7.2.
    • If you chose C: That puts the point at 0 seconds, on the up line. Go across to the time first, then up. Go to S3.7.2.

  5. Tariq walks 30 m away from home in 10 s. He stands still for 10 s. Then he walks 5 m farther from home in 20 s. What does his distance and time graph look like?

    Tap your answer.

    1. Not this one. Standing still makes his speed 0, not his distance. He stays 30 m from home, so the line stays flat at 30 m. Go to S3.7.2. Try another.

    2. Not this one. You swapped fast and slow. The first part covers more distance in less time, so it is the steeper line. Go to S3.7.2. Try another.

    3. Not this one. The last part covers a short distance in a long time. That is slow, so the last line is gentle, not steep. Go to S3.7.2. Try another.

    4. Yes, that is right. First he goes at 3 m/s, which is the steepest part. Then his speed is 0 m/s, so the line is flat. Last he goes at 0.25 m/s, a gentle climb.

    See the answer

    It climbs steeply, then goes flat, then climbs gently.

    First he goes at 3 m/s, which is the steepest part. Then his speed is 0 m/s, so the line is flat. Last he goes at 0.25 m/s, a gentle climb.

    • If you chose A: Standing still makes his speed 0, not his distance. He stays 30 m from home, so the line stays flat at 30 m. Go to S3.7.2.
    • If you chose B: You swapped fast and slow. The first part covers more distance in less time, so it is the steeper line. Go to S3.7.2.
    • If you chose C: The last part covers a short distance in a long time. That is slow, so the last line is gentle, not steep. Go to S3.7.2.

  6. At 4 s a walker is 6 m from home. At 10 s the walker is 21 m from home. What is the speed between these times?

    See the answer

    2.5 m/s

    Distance covered = 21 − 6 = 15 m. Time = 10 − 4 = 6 s. Speed = 15 ÷ 6 = 2.5 m/s.

  7. From an earlier chapter

    Review: Tariq runs 60 m in 12 s. What is his speed?

    Tap your answer.

    1. Not this one. You added the two numbers. Speed is distance divided by time. Go to S3.7.1. Try another.

    2. Not this one. You divided time by distance. Put the distance first: distance ÷ time. Go to S3.7.1. Try another.

    3. Yes, that is right. Speed = distance ÷ time = 60 ÷ 12 = 5 m/s.

    See the answer

    5 m/s

    Speed = distance ÷ time = 60 ÷ 12 = 5 m/s.

    • If you chose A: You added the two numbers. Speed is distance divided by time. Go to S3.7.1.
    • If you chose B: You divided time by distance. Put the distance first: distance ÷ time. Go to S3.7.1.

Keep it

Copy this into your exercise book.

A distance and time graph has time across and distance from home up. A flat line is still. A steeper line is faster. A line going down is coming back home.

Draw: Axes marked 0 to 60. A line that climbs steeply, goes flat, then climbs gently. Write fast, still, slow.

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.