Lesson focus: Changing gradients and horizontal sections tell the story of a journey from a fixed start.
Interpret a staged journey and distinguish final distance from total path length.
Build on earlier learning
Motion graphs: distance and timeThis lesson applies gradient to stops, speed changes and returns.
You will be successful when you can…
- Identify moving and stationary intervals.
- Compare gradient magnitude.
- Recognise a return.
- Calculate total path length.
Words that carry the science
- stationary
- Not changing position relative to the reference.
- interval
- A section between two times.
- return journey
- Motion back toward the start.
- gradient magnitude
- The size of a gradient without its sign.
- total distance
- The sum of all path sections.
Each section represents one stage
01Each section represents one stage
On a distance-from-start graph, rising means moving farther away, horizontal means stationaryNot moving. and falling means returning closer.
The plotted line is a relationship between measurements, not the physical route or a hill.
02Gradient magnitude compares speed
A steeper section has greater speed. A returning section has negative gradient, but speed is reported as its positive magnitude.
Corners model changes as instant; real objects take time to change speed or direction.
03Total distance includes every stage
Going 300 m out and 200 m back gives 500 m total distanceThe whole distance travelled on a journey, adding all the parts together. and a final distance of 100 m from the start.
Do not use the final graph height as total distance. Area beneath a distance–time graph has no standard motion meaning.
Distance–time graph
Set the speed for each 10 s stage and move the time slider. A steeper line means a greater speed; a flat line means stationary.
Controls
Read a staged journey
A walker reaches 300 m in 5 min, waits to 8 min, then returns to 100 m by 12 min.
- Outward speed = 300 ÷ 5 = 60 m/min.
- The stop lasts 3 min.
- Return speed = 200 ÷ 4 = 50 m/min.
- Total distance = 300 + 200 = 500 m.
How to make the reasoning visible: The walker covers 500 m and finishes 100 m from home.
Decode the journey
Use distance from home for each stage.
| Stage | Time / min | Start / m | End / m |
|---|---|---|---|
| A | 0–4 | 0 | 240 |
| B | 4–7 | 240 | 240 |
| C | 7–9 | 240 | 120 |
| D | 9–15 | 120 | 300 |
Calculate each moving speed.
Find total distance and final distance.
Check your understanding
Answer from memory, then check against the suggested answer.
What does a horizontal section show?
What does a falling line show?
How is section speed found?
Compare gradients +3 m/s and −5 m/s.
Why is position–time more informative on a line through the origin?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
The distance–time graph shows a walk away from home and part of the way back.
Calculate the speed on the way out, from 0 to 5 min.
(1)What happens between 5 and 7 minutes?
(1)Calculate the speed on the way back, from 7 to 10 min.
(1)Calculate the total distance walked.
(1)How far from home is the walker at 10 min?
(1)Total for this question: 5 marks
Command word: For analyseA command word: look closely at information or data and pick out the patterns and important details., combine descriptions with numerical evidence.