Year 9 Science · Unit 4 · Lesson 15
Challenge Worksheet
Learning Goals
Two graphs — same journey
The distance-time graph (left) and speed-time graph (right) below describe the same journey: a cyclist accelerates from rest, rides at constant speed, then brakes to a stop. Answer the three questions below.
1. What information does the speed-time graph give you that the distance-time graph does NOT directly show? Give one specific example from the graphs above.
2. From the speed-time graph: estimate the total distance travelled between t = 0 and t = 28 s. Show how you calculated the area under each section (triangle + rectangle + triangle).
3. Explain in words why the area under the speed-time graph equals the gradient (slope) concept applied to the distance-time graph. What is each one actually measuring?
Find the mistake — four errors in one motion analysis
A student wrote this motion analysis
"A cyclist rode 6 km east then 4 km north, so their displacement was 10 km. From the distance-time graph of this journey, I can read off the acceleration at any point — the gradient tells me how fast they are speeding up. During a rest stop, the speed-time graph shows a horizontal line, which means they are stationary. Finally, I calculated the acceleration as 5 m/s because they went from 0 to 5 m/s in one second."
1. The student claims displacement = 10 km. Identify the error and write the correct displacement. Show your calculation.
2. The student says the gradient of a distance-time graph gives acceleration. Correct this error and explain what the gradient of each graph type actually gives.
3. The student says a horizontal line on a speed-time graph means the object is stationary. Correct this error and explain what it actually means.
4. The student states acceleration is "5 m/s". What is wrong with this answer? Write the correct value with correct units.
Wrap Up
In one sentence, what was the main idea of this lesson?