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Distance–time graphs GCSE lesson: speed as gradient, reading a journey

Name: ____________________ Date: ____________________

Show your working. Check every root by substitution and label your sketches.

Distance–time graphs: practice

Show your working on paper. Give speeds in km/h unless the question says otherwise. The stretch is optional.

Diagnostic question: choose and explain

  1. Kai's distance–time graph goes from (0, 0) to (0.5, 4), stays flat to (1.5, 4), then goes to (3.5, 8). Time is in hours, distance in km. When was Kai fastest?
    1. From 1.5 to 3.5 hours
    2. From 0 to 0.5 hours
    3. From 0.5 to 1.5 hours
    4. The two moving parts tie: 4 km each

Practice questions

  1. A cyclist rides 36 km in 3 hours at a steady speed. What is her speed in km/h?
  2. A straight line on a distance–time graph goes from (0, 0) to (4, 10). Time is in hours, distance in km. What is the speed in km/h?
  3. Mo walks 3 km in 45 minutes. What is his speed in km/h?
  4. A car travels at 48 km/h for 20 minutes. How many km does it go?
  5. On a distance–time graph (hours, km from home), a straight line goes down from (2, 6) to (4, 0). What is happening?
    1. Slowing down to a stop
    2. Going downhill
    3. Coming back home at 3 km/h
  6. Two friends walk along the same road from the same house. Their lines on one distance–time graph cross at (2, 6). What does the crossing mean?
    1. They are walking at the same speed
    2. After 2 hours both are 6 km from the house: one passes the other
    3. They have both stopped
  7. Which is faster: 20 km in 30 minutes, or 50 km in 1 hour 15 minutes?
    1. 20 km in 30 minutes
    2. 50 km in 1 hour 15 minutes
    3. They are the same speed
  8. Sam drives 90 km in 1.5 hours, stops for 30 minutes, then drives 60 km in 1 hour. What is his average speed for the whole journey, in km/h?
  9. A distance–time graph is a curve that gets steeper and steeper. What is happening?
    1. Slowing down
    2. Speeding up
    3. Going up a steeper and steeper hill
  10. Stretch: Ana leaves home walking at 3 km/h. Ben leaves the same place an hour later, along the same path, at 5 km/h. He catches her ___ hours after Ana set off, ___ km from home.

Support: For question 3: change the minutes into hours first, 45 ÷ 60. Then speed = distance ÷ time. For question 5: ask what the distance from home is doing.

Distance–time graphs: exit

A sketch on paper, then your speed and one sentence.

  1. You walk 3 km from home in 1 hour, stop for 30 minutes, then walk home in 45 minutes. Sketch the distance–time graph. What is your speed on the way home? Say how the graph shows which part was fastest.

Exit check

One sketch from a story and one speed show who reads and draws these graphs.

Walk 3 km from home in 1 hour, stop for 30 minutes, then walk home in 45 minutes. Sketch the distance–time graph.

Distance–time graphs: speeds and journeys

Show your working, and give units with every speed. Change minutes into hours first. Draw the graph in question 3 on squared paper, time across and distance up.

1. A bus travels 30 km in 45 minutes. What is its speed in km/h?

2. How long does it take to walk 15 km at 6 km/h? Give your answer in hours and minutes.

3. Lee leaves home at 9 am and cycles 12 km to the park at 8 km/h. He stays for 30 minutes, then cycles home at 12 km/h. Draw the distance–time graph. When does he get home?

4. A distance–time graph (hours, km) goes from (0, 0) to (2, 6), is flat to (3, 6), then goes down to (4, 0). Describe the journey, with the speed of each part.

5. Ali leaves the house at 12:00, walking at 4 km/h. Bea leaves the same house at 12:30, cycling the same way at 12 km/h. At what time does Bea catch up with Ali, and how far from the house?

6. A driver goes 40 km at 80 km/h, then another 40 km at 40 km/h. Show that the average speed for the 80 km is not 60 km/h.

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