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GRAPHS · LESSON 04

Distance–Time Graphs

Turn a journey into a visual story of movement, stopping and speed.

⏱️ 15–18 min 📘 Developing ✏️ Worked examples included

Learning Objectives

Introduction

This lesson develops Distance–Time Graphs from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.

Key Notes

Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.

🤔 Think About This...

A learner walks away from home, stops at a shop and then continues walking.

How could one picture show the whole journey without drawing the road?

A distance–time graph records how far the learner is from the starting point at each moment.

🚌

Follow a Harare–Chitungwiza Journey

Move the time control and watch how the traveller's position changes.

Reading a Distance–Time Graph

Key idea: The horizontal axis shows time. The vertical axis shows distance from the starting point.

Rising straight line

The object is moving at a constant speed.

Horizontal line

Time is passing, but distance is not changing. The object is stationary.

Steeper line

Distance changes more quickly, so the object is moving faster.

Downward line

The object is returning towards the starting point.

Speed Is the Gradient

speed = change in distance ÷ change in time

A cyclist travels 12 km in 40 minutes.

1

Change in distance = 12 km.

2

Change in time = 40 minutes.

3

Speed = 12 ÷ 40 = 0.3 km per minute.

4

In km/h: 0.3 × 60 = 18 km/h.

Check the time unit before calculating. Minutes and hours cannot be mixed without conversion.

Worked Example: Describing a Journey

A graph rises from 0 km to 4 km in 20 minutes, remains horizontal for 10 minutes, then rises to 10 km by 50 minutes.

  1. The traveller moves 4 km in the first 20 minutes.
  2. The traveller rests for 10 minutes.
  3. The traveller then covers another 6 km in 20 minutes.
  4. The second moving section is steeper, so it represents a higher speed.

⚠️ Common Mistake

A distance–time graph is not a drawing of the road. A rising line does not mean the traveller is climbing a hill.

✅ Quick Check

What does a horizontal section mean?
Which of two straight sections represents the faster speed?
A bus travels 90 km in 1.5 hours. Find its speed.

🧠 Let’s Think Together

Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.

Practice Questions

Foundation
  1. Explain what each axis represents on a distance–time graph.
  2. Describe the meaning of a horizontal line.
  3. Calculate the speed of a runner who travels 400 m in 80 seconds.
Developing
  1. A car covers 60 km in 45 minutes. Calculate its speed in km/h.
  2. Draw a graph for a 30-minute journey: travel 3 km in 10 minutes, stop for 5 minutes, then travel another 6 km in 15 minutes.
Challenge
  1. Explain why a vertical section would be impossible on a normal distance–time graph.

✅ Check Your Work

Attempt the questions before opening the solutions.

Show answers and working

Foundation

  1. Horizontal axis: time. Vertical axis: distance travelled from the start.
  2. The object is stationary because time passes but distance does not change.
  3. Speed=400÷80=5 m/s.

Developing

  1. 45 minutes=0.75 h, so speed=60÷0.75=80 km/h.
  2. Plot (0,0) to (10,3), then horizontally to (15,3), then to (30,9).

Challenge

  1. A vertical line would mean distance changes while no time passes, requiring infinite speed.

Common Mistakes

Exam Focus

Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.

Summary