Describing motion · Investigation
Distance–time graphs
Someone walks 6 m down a level corridor, waits at a door, then runs the last 12 m. Drawn as a graph, that journey rises, goes flat, then rises much more steeply — and the floor never changed height. So what is the height of the line telling you?
Start here
The line climbs. The corridor is flat.
Someone walks 6 m down a level corridor, waits at a door, then runs the last 12 m. Drawn as a graph, that journey rises, goes flat, then rises much more steeply. The floor never changed height.
So what is the height of the line telling you?
The upright axis is distance from the start. It only comes down if you come back. Speed is not plotted anywhere on this graph — it is hiding in the steepness, and that is the only place it lives.
Each point is one reading: at this time, that far from the start. Join the readings and the whole journey is in one picture — including the parts where nothing happened.
Plot the sensor's readings yourself
Seven readings, two seconds apart
A motion sensor at the start of the corridor recorded the distance every two seconds. Put each reading on the grid, in order. The one you are looking for is named under the graph.
Looking for:
Between 4 s and 8 s, what was the walker doing?
Which part of the journey was fastest?
What was the speed over the last four seconds?
Seven readings, one line, and a whole journey — including four seconds in which nothing happened at all.
Key fact
On a distance–time graph, the steepness of the line is the speed. A flat line is not slow. It is stopped.
Build the journey that draws this line
Walk the graph
The dashed line is the target. Choose what happens in each three-second block, then send the walker down the corridor and watch the line draw itself.
Seconds 0 to 3
Seconds 3 to 6
Seconds 6 to 9
Seconds 9 to 12
Your line and the target are compared at the end point only, as two numbers. Whether that counts as a match is your call, not the page's.
Think again
“The line goes up, so she is cycling uphill — and where it comes back down she is freewheeling down the other side.”
A cyclist rides 400 m to the postbox, posts a letter, and rides home. Her graph rises, goes flat, then falls back to zero — and the road is flat the whole way. The falling section is the ride home. Her distance from the start is getting smaller, which is the only thing that axis can mean. When the line reaches zero she is back where she began.
There is no room for a hill on this graph. It holds two quantities and no others: how long, and how far from the start. The road could be flat, uphill, or a spiral staircase, and the graph would be identical.
“A curved line means the object is going round a bend.”
A distance–time graph knows nothing about direction in space — the only thing the axes carry is how far along the journey and how long it has taken. A curve means the gradient is changing, and the gradient is the speed, so a curve means speeding up or slowing down. An object going round a perfect bend at a steady speed draws a straight line here.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Recall
A distance–time graph is horizontal between 20 s and 35 s. What was happening in those fifteen seconds?
Rung 2 · The one that catches people
Two journeys are drawn on the same axes. Line A is steeper than line B. Which statement must be true?
Rung 3 · Explain
A graph rises steeply, then flattens, then rises gently. Describe that journey in words and say how you know each part, without using the words up or down.
Rung 4 · Take it somewhere new
A lift rises 30 m in 20 s, waits 10 s, then returns to the ground floor in 15 s. Describe the graph of its distance from the ground floor against time, giving the speed of each moving part with units. Then say how the graph would differ if you plotted total distance travelled instead.
Key note
A distance–time graph plots distance from the start against time. Steeper means faster, flat means stopped, and a line coming back down means returning towards the start. It records a journey; it never draws the route.
Going further
Change the upright axis from distance from the start to total distance travelled and the same journey gives a different line — one that can never come down, because a distance you have already travelled cannot be un-travelled. The cyclist's ride home now climbs to 800 m instead of falling to zero. Two graphs, one journey, and only one of them can tell you that she got home.
Before this lesson
At GCSE this becomes
- Gradients of curved graphs, motion graphs where a value can be negative, and the area underneath them.
Where to next
Ask Mr Badmus AI
Not sure why a flat line means stopped?
Lesson content © MrBadmusAI.