Lesson overview
Speed and motion graphs: How can a graph tell the story of a journey?
Plan a motorised trolley’s journey from a target graph and run it in front of a motion sensor: its live distance–time line should land on the target. Then predict how far it goes from the area under a speed–time graph, and watch the area fill in.
Suggested sequence
- Lesson 1 · The story of a journey. Speed, velocity and average speed; reading distance–time graphs and finding speed from the gradient. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- Lesson 2 · The area under the line. Speed–time graphs, and the distance travelled from the area under the line. Read together (10–15 min), show or explore the experiment (10 min), practise with self-checking (15–20 min).
- End of module · final check. 2 new questions, 20–30 min, without hints or notes; pupils check their answers once they have answered them all.
- One to two weeks later · return questions. 2 questions, 15 min, lesson closed.
Learning goals
Part 1: The story of a journey
- Define speed as distance travelled per unit time and use v = s/t; define velocity as speed in a given direction (1.2.1, 1.2.2)
- Use average speed = total distance travelled ÷ total time taken (1.2.3)
- Sketch, plot and interpret distance–time graphs, and tell from a graph or from data when an object is at rest, moving at constant speed, speeding up or slowing down (1.2.4, 1.2.5)
- Calculate speed from the gradient of a straight-line section of a distance–time graph (1.2.6)
Part 2: The area under the line
- Sketch, plot and interpret speed–time graphs, and tell from them when an object is at rest, moving at constant speed, speeding up or slowing down (1.2.4, 1.2.5)
- Calculate the area under a speed–time graph to find the distance travelled for constant speed or constant acceleration (1.2.7)
Misconceptions to listen for
- “Speed = time ÷ distance = 5 m/s.” — That is the number of seconds for each metre. Speed is metres per second: divide the distance by the time.
- “Speed = distance × time = 7.2 m/s.” — Multiplying gives a bigger number for a slower trolley that takes longer. Divide the distance by the time.
- “They have the same velocity because they move at the same speed.” — Velocity includes the direction. Opposite directions mean different velocities, even at the same speed.
- “B has a speed of −0.3 m/s.” — Speed has no direction and is never negative. The minus sign belongs to B's velocity.
- “Leave out the minute at the lights: 1500 m ÷ 240 s = 6.3 m/s.” — The journey took 5 minutes from start to finish. Average speed uses the total time, stops included.
- “Average the two riding speeds: (5 m/s + 7.5 m/s) ÷ 2 = 6.3 m/s.” — That ignores the stop and the time spent at each speed. Use total distance ÷ total time.
- “D is slowing down because the line goes down.” — A falling line on a distance–time graph means the distance from the start is getting smaller: she is coming back. Slowing down would make the line flatter.
- “C is a steady speed because the line is straight.” — A flat line means the distance isn't changing at all: she is at rest.
- “Start the graph at 0 m.” — The dog starts 2 m from its owner, so the line starts at 2 m on the distance axis.
- “Draw the running part as a curve.” — At a steady speed the distance grows by the same amount every second, so the line is straight.
Scope
Speed as distance travelled per unit time, v = s/t (1.2.1); velocity as speed in a given direction (1.2.2); average speed = total distance ÷ total time (1.2.3); sketching, plotting and interpreting distance–time and speed–time graphs (1.2.4); at rest, constant speed, speeding up and slowing down from a graph or from data (1.2.5); speed from the gradient of a straight section of a distance–time graph (1.2.6); distance travelled from the area under a speed–time graph for constant speed or constant acceleration (1.2.7). Acceleration as a number, free fall and drag (1.2.8–1.2.13) are in MOT02.