Lesson focus: A motion graph links measured distance and time; its gradientHow steep a line on a graph is. represents a rate of change.
Plot distance–time data and calculate speed from a straight-line gradient.
Build on earlier learning
SpeedThe speed equation becomes the graph-gradient calculation.
You will be successful when you can…
- Label suitable axes.
- Plot coordinates accurately.
- Calculate a large-triangle gradient.
- Relate steepness to speed.
Words that carry the science
- axis
- A reference line carrying a variable, scale and unit.
- gradient
- Vertical change divided by horizontal change.
- origin
- The point where both values are zero.
- constant speed
- Equal distances covered in equal times.
- best-fit line
- A line representing the overall pattern in measured data.
A graph communicates measurements
01A graph communicates measurements
Place time on the horizontal axisOne of the two lines on a graph, labelled with the quantity and its unit. and distance on the vertical axis. Label quantity and unit, choose a linear scale and use most of the plotting area.
Join points for a known continuous journey; use a best-fit lineA straight line or smooth curve drawn so the points are spread evenly on either side of it, showing the overall pattern. when repeated experimental measurements scatter.
02Gradient gives speed
For a straight section, gradientHow steep a line on a graph is. = change in distance ÷ change in time. Use two well-separated points and retain axis units.
A steeper positive gradient represents a greater speed. A horizontal section has zero speed.
03The label determines the meaning
A total distance travelled–time graph cannot fall because accumulated path length never decreases. A distance from a start–time graph can fall during a return.
Read the vertical label before interpreting. Height does not show speed; gradient does.
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
Gradient of a journey section
A line runs from 20 m at 5 s to 80 m at 20 s.
- Select (5 s, 20 m) and (20 s, 80 m).
- Distance change = 60 m.
- Time change = 15 s.
- Gradient = 60 ÷ 15 = 4 m/s.
How to make the reasoning visible: The constant speedMoving at the same speed all the time, covering equal distances in equal times. is 4 m/s.
Construct a distance–time graph
Plot and compare the four data sets.
| Series | 0 s | 5 s | 10 s | 15 s |
|---|---|---|---|---|
| A / m | 0 | 15 | 30 | 45 |
| B / m | 0 | 10 | 20 | 30 |
| C / m | 0 | 20 | 40 | 40 |
| D / m | 0 | 5 | 20 | 45 |
Graph skills: SLAPUK and choosing a scaleDistance–time graphs start with a good scale.
Which series has constant speed 3 m/s?
What makes D different?
Check your understanding
Answer from memory, then check against the suggested answer.
Which axis carries time?
What does gradient represent?
What shows constant speed?
How can a gradient from scattered data be made more reliable?
Why can total distance travelled never fall?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
Determine the speed shown by the line. Show your working.
(3)What does the straight line show about the motion?
(1)Total for this question: 4 marks
Command word: For determineA command word: work out an answer from the information or data you are given., extract values accurately and show the gradient calculation.