Describing Motion Around Us · Lesson 5 of 10
Graphical Representation of Motion
“Motion graphs let moving objects leave behind neat little stories.”
• Explain why motion is represented with graphs. • Place time and position on appropriate axes. • Choose and state a useful scale. • Plot ordered pairs accurately. • Distinguish a motion graph from a route map. • Relate straight and curved graphs to different motion patterns.
A table can list a vehicle’s position every second, but a graph lets the pattern appear at a glance. Equal rises, changing rises and periods with no change become shapes. A graph is therefore not decoration; it is a compact language for describing how one physical quantity depends on another.
Motion graphs can show position, velocity or acceleration against time. They help compare objects, calculate physical quantities and identify whether motion is uniform or changing. In the straight-line cases considered here, time is placed on the horizontal axis and the changing motion quantity on the vertical axis.
Plotting graph
| Graph element | Purpose |
|---|---|
| Origin | Common starting point of the axes |
| Horizontal axis | Shows time |
| Vertical axis | Shows position or velocity |
| Scale | Connects graph divisions with physical values |
| Plotted point | Represents one pair of measured values |
| Line or curve | Shows the pattern connecting the data |
Activity: Let us plot a graph
Consider a vehicle at positions 0, 20, 40, 60, 80, 100 and 120 metres at times 0, 1, 2, 3, 4, 5 and 6 seconds. Each time-position pair becomes one point. A suitable scale could assign equal horizontal spacing to each second and equal vertical spacing to each 20 metres.
Problem
Plot the given time-position pairs and describe the result.
- 1.Draw perpendicular axes and label the horizontal axis Time (s).
- 2.Label the vertical axis Position (m).
- 3.Choose scales that fit all values and use much of the space.
- 4.Plot ((0,0),(1,20),(2,40),(3,60),(4,80),(5,100),(6,120)).
- 5.Join the points. They lie on a straight line because position increases by an equal amount each second.
Problem
Positions at 0, 2, 4, 6, 8, 10 and 12 s are 0, 1, 4, 9, 16, 25 and 36 m. What shape is expected?
- 1.Put time on the horizontal axis and position on the vertical axis.
- 2.Choose scales that include 12 s and 36 m.
- 3.Plot all seven ordered pairs.
- 4.The position increases by larger amounts in successive equal time intervals.
- 5.The points do not form a straight line; a smooth curve represents the changing rate.
Ready to Go Beyond
A line drawn between measured points suggests possible intermediate values. For constant-velocity data, intermediate points on the straight segment are consistent with the model. If motion changed unpredictably between measurements, the joined line would be an assumption rather than a direct observation.
Note
A motion graph is not a route map. A rising line does not mean that the road physically slopes upward. It means the vertical-axis quantity increases as time passes. The axes describe quantities, not compass directions or road shapes.
A graph without labelled axes, units and scale cannot be interpreted quantitatively. Do not choose a scale merely because its numbers are easy; it should also use the available space well.
Quiz
Which statement is a key takeaway from this lesson?
Which additional statement is also a key takeaway from this lesson?
Which further statement is also a key takeaway from this lesson?
Which another statement is also a key takeaway from this lesson?
Which final statement is also a key takeaway from this lesson?
Practice Problems
- Plot positions 0, 5, 10, 15 and 20 m at times 0, 1, 2, 3 and 4 s.
- Explain why time is placed on the horizontal axis.
- Describe two problems caused by a poor scale.
- Explain why a steep graph line does not mean a steep road.
Key Takeaways
• A graph displays how one physical quantity changes with another. • Time is shown on the horizontal axis. • Position or velocity is shown on the vertical axis. • Every graph needs labels, units and scale. • Graph shape describes motion, not the physical route.