Plotting and Interpreting Distance-Time Graphs

Lesson 6 of 6: Distance, Time and Speed

In this lesson:

• Plot a distance-time graph from data in 5 steps
• Interpret sections of a journey from the graph
• Calculate speed for each section and average speed

What You Will Learn Today

By the end of this lesson:

1. Plot distance-time graphs from given data
2. Draw straight lines using a ruler
3. Interpret journeys including rest and moving sections
4. Calculate speed from each graph section
5. Solve problems using distance-time graphs
6. Apply all three formulae to real-life contexts

Review: Turning Data into a Graph

A cyclist's journey (time on x-axis, distance on y-axis):

How do we turn this table into a graph?

Steps 1-2: Axes, Labels, and Scale

Step 1: Draw and label both axes with units.
Step 2: Scale — time: 0–4 hr · distance: 0–40 km

Step 3: Plot Each Point from the Table

Each row of the data table becomes one coordinate (time, distance):

• Row 1: (0, 0) — start
• Row 2: (1, 10) — after 1 hour
• Row 3: (2, 20) — after 2 hours
• Row 4: (3, 20) — still 20 km ← resting!
• Row 5: (4, 35) — after 4 hours

Plot each point. Mark it clearly with a small dot.

Steps 4-5: Join Points, Interpret Journey

Use a ruler. Join points in order with straight lines.

The Cyclist Journey: Full Graph

Three sections: moving → resting → moving faster

Guided Practice: Plot Your Own Graph

Plot this journey in your exercise book:

Follow all five steps. Choose a scale for 0–50 km. Use a ruler.

Quick Check: Your Graph Has Three Sections

Describe what your graph shows:

• What happened between hours 1 and 2?
• What happened between hours 2 and 3?
• Which section looks steeper — hours 0-2 or hours 3-4?

Answer all three before advancing.

Quick Check: Interpreting the Three Sections

• Hours 1–2: moving — line is rising
• Hours 2–3: resting — line is horizontal (distance = 30 km throughout)
• Hours 3–4: steeper — faster speed than hours 0–2

The steeper the line, the faster the speed.

Key Concept: Use Distance Change, Not Endpoint

For section speed — use the CHANGE in distance:

Example: section from 20 km to 35 km in 1 hour:

Worked Example: Section Speed Calculation

Cyclist graph — Section 1 (0 to 2 hours):

Section 2 (2–3 hours): resting → speed = 0 km/hr

Worked Example: Comparing Section Speeds

Section 3 (3 to 4 hours):

Compare: Section 1 = 10 km/hr · Section 3 = 15 km/hr → faster!

Average Speed: Total Distance, Total Time

Average speed ≠ mean of all section speeds.

Cyclist: total distance = 35 km, total time = 4 hours

This includes the rest period — rest reduces average speed.

Quick Check: Matatu Average Speed

A matatu journey: 50 km in hour 1, 50 km in hour 2, rest in hour 3, 40 km in hour 4.

• Total distance?
• Total time?
• Average speed?

Calculate before advancing.

Quick Check: Matatu Average Speed Answer

Total distance = 50 + 50 + 0 + 40 = 140 km

Total time = 4 hours

Rest period: 0 km added, but 1 hour counted.

Practice: Full Boda-Boda Graph Problem

Boda-boda journey: (0,0), (1,30), (2,60), (3,60), (4,80)

1. Plot the graph (draw axes, choose scale, plot, join, interpret)
2. Speed during hours 0–2?
3. Speed during hours 3–4?
4. Total distance? Average speed for whole journey?

Show all working. Write units.

Practice: Full Graph Problem Answers

2. Section 0–2:
3. Section 3–4:
4. Total = 80 km · Average =

First section fastest (30 > 20 km/hr; steeper slope).

Topic 8 Complete: Key Reminders

✓ Three formulae: · ·

✓ Plot in 5 steps: axes → scale → points → ruler lines → interpret

✓ Speed for a section = distance change ÷ time

Average speed = total distance ÷ total time (not mean of speeds)

Scale must be equal intervals · use a ruler for straight lines

Label axes with units · plot (time, distance) not (distance, time)

Applying Distance, Time and Speed Daily

These skills appear in real life every day:

• Planning a journey from Kampala to Entebbe
• Knowing what time a bus will arrive
• Understanding speed limits on Ugandan roads
• Calculating running speed for sports
• Tracking delivery times for goods

Congratulations on completing Topic 8!