Describing movement
Distance/time graphs
Scientists use graphs to describe how two variables are related. We can use graphs to describe the movement of an object.
One way to do this is to plot distance on the vertical axis and time on the horizontal axis. A graph like this is called a distance/time graph.
Graphs are more useful than words for describing movement because:
- it is easier to see trends and patterns
- you can read any value of distance or time during the journey
- other values, such as speed, can be calculated from the graph
- information about the whole journey can be seen easily
This distance/time graph shows a car’s journey from point A to C, and back again. The journey has four sections:
- The car travels at a constant speed from A to B. The graph is a straight, upward sloping line.
- The car is stationary at B. This appears as a flat, horizontal line. The car is not moving, but time continues.
- The car travels faster from B to C — a steeper slope shows this higher speed.
- From C to A, the car returns at a constant speed. The distance decreases over time, so the line slopes downward.
You can sketch distance/time graphs without numbers. A sketch shows shape, not scale.
Worked example
This graph shows a short train journey between stations P and R, 2000 m apart:
- The train leaves station P at time 0
- It takes 200 s to reach R
- It stops at R for 140 s
- Then returns to P in 100 s
a. The distance is 2000 m and the time taken is 200 s.
speed = distance ÷ time
= 2000 ÷ 200
= 10 m/s
b. The distance is 2000 m and the return time is 440 − 340 = 100 s.
speed = distance ÷ time
= 2000 ÷ 100
= 20 m/s
| Phase | Action | Time (s) | Distance (m) | Speed (m/s) |
|---|---|---|---|---|
| P to R | Moving | 200 | 2000 | 10 |
| At R | Stationary | 140 | 0 | 0 |
| R to P | Moving (faster) | 100 | 2000 | 20 |
Check your understanding: If the train took 300 seconds to return instead of 100, what would its speed be?
Show Answer
speed = 2000 ÷ 300 = 6.67 m/s
Questions
Show Answer
A straight line sloping upwards from the origin, showing distance increasing steadily over time.
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Draw a line steeper than the first one, also starting at the origin, and label it ‘faster’.
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Draw a line less steep than the original, starting from the origin. Label it ‘slower’.
For the first part of the journey, he rides his bicycle at a constant speed.
Marcus then stops to talk to a friend.
For the last part of the journey, he continues to ride his bicycle at a
slower constant speed than before until he arrives at the shop. Sketch a distance/time graph for Marcus’s journey.
Show Answer
Draw three segments: first a straight upward slope (constant speed), then a flat horizontal line (stopped), then a less steep upward slope (slower speed).
Show Answer
Label the three sections: “Riding fast”, “Stopped”, “Riding slowly”.
How far did the boat travel when crossing the lake once?
Show Answer
80 meters — this is the peak distance reached on the graph before the boat stops.
Show Answer
Speed = distance ÷ time = 80 m ÷ 40 s = 2 m/s
Show Answer
50 seconds — the flat section of the graph spans from 40 s to 90 s.
Show Answer
Speed = 80 m ÷ 40 s = 2 m/s — same as the first time.
Show Answer
Total time = 40 s (out) + 50 s (stopped) + 40 s (return) = 130 seconds.
Think Like a Scientist
Walking and running
In this activity, you will plan an investigation, make measurements, do calculations and draw a distance/time graph.
- space where you can run safely
- tape measure
- stopwatch
- one sheet of graph paper per person
- Plan what measurements you will need to make and how you will make these measurements.
- Make a list of the safety precautions that the person who is running should take.
- Make your measurements safely and record them in a suitable way.
Show Answer
Average speed = total distance ÷ total time. For example, 20 m ÷ 16 s = 1.25 m/s.
Show Answer
Use the same formula: speed = distance ÷ time. For example, 20 m ÷ 6 s = 3.33 m/s.
Show Answer
Plot time on the horizontal axis and distance on the vertical axis. Use two lines with different labels: one for walking, one for running. The running line should have a steeper gradient.
Show Answer
The running line is steeper, which shows a faster speed. For the same time, the person running covers more distance than the person walking.
- Decide how confident you are about each of these statements. Give yourself 5 if you are very confident and 1 if you are not confident at all.
- I made useful contributions to planning.
- I made useful contributions to making the measurements.
- I drew my graph carefully, neatly and accurately.
- Which do you think is better:
- drawing a distance/time graph for a journey, or
- describing a journey in words?