Mathematics 7–10 · Years 7–8
Rates from timed walking: a distance-time graph from real data
Number and algebra
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The idea
Speed is a rate, distance per unit time, and it appears as the gradient of a distance-time graph drawn from stopwatch readings taken at measured marks.
Safety card
Hazards
- collisions on the course
- uneven ground
- sun exposure
Controls
- one walker on the course at a time
- flat clear surface
- hats
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's excursion and playground supervision rules.
What you need
- 20 m tape measure and 5 cones or chalk marks at 0, 5, 10, 15 and 20 m
- 5 stopwatches (or phones): 4 timers standing at the 5, 10, 15 and 20 m marks, and a second watch for the 10 m timer in the stop-and-go trial
- Recording table with columns distance (m) and time (s)
- Grid paper
How to do it
- Mark a straight 20 m course on flat ground with marks every 5 m.
- One walker starts on go; every timer stops their watch as the walker passes their mark. Record the four times.
- Repeat for a slow walk, a brisk walk and a jog, and once for a walk that stops for 5 s at the 10 m mark; in that trial the 10 m timer stops one watch as the walker arrives and the second as the walker leaves, giving two points at 10 m.
- Plot distance against time for each trial on the same axes and join the points.
- Compute the gradient of each line in m/s (rise over run) and convert to km/h by multiplying by 3.6.
- Describe the stop-and-go trial from the shape of its graph and compute the average speed over the whole 20 m.
What you should see
Steady walking gives points close to a straight line through the origin; a walker covering 20 m in 14.3 s has a gradient of 1.40 m/s, which is 5.04 km/h (1.40 × 3.6). A jog gives a steeper line, and the trial with a 5 s stop shows a flat segment at 10 m between the arrival and departure times (7.1 s and 12.1 s at 1.40 m/s) and a lower average speed than its moving gradient. Timers at successive marks give times that increase; small kinks come from each timer's reaction time in stopping the watch. The learner knows it worked when the gradient from the graph matches 20 m divided by the final time within 5 per cent.
What changes
- What you change
- time
- What you measure
- distance from the start
- What you keep the same
- same course
- same walker within a trial
- timers start on the same signal
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A steeper distance-time line means the walker is further away rather than faster.
- A flat segment means the walker is moving at a steady speed.
- km/h and m/s can be compared without conversion.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Ratios and rates; page read 2026-09-22MA4-RAT-C-01
- Australian Curriculum v9AC9M8M05AC9M7A04AC9M8A03
Sources
The pages the author read to write this activity.