GCSE · Physics · Edexcel · Spec 1PH0

Distance/time graphs

One line on a graph can tell you exactly when something moved, when it stopped, and how fast it went.

Follow Jo's scooter ride

Time (s): 50. Distance travelled (m): 50

Drag the dot along Jo's ride (the numbers are made up for this example). The first number is the time, the second is how far Jo has gone. Where does the second number stop climbing? Where does it climb fastest?

Watch out: Higher up the graph doesn't mean faster. The first 25 s and the last 25 s sit at very different heights, but the line is equally steep in both — so Jo is going at the same speed in both. Judge speed by steepness, never by height.

What does a flat line really mean?

A hiker's distance/time graph slopes upwards for a while, then runs perfectly flat for 10 minutes, then slopes upwards again — more steeply than before.

What was the hiker doing during the flat part? Pick the idea closest to what you think.

Walking along a flat bit of path — and the steeper bit afterwards is where they climbed a hill.Walking at a steady speed — a flat line means the speed isn't changing.Covering a lot of ground — the line goes a long way across the page.Standing still — the minutes kept ticking by, but the distance didn't go up at all.

How sure are you?

I'm sureI think soI'm guessing

Walking along a flat bit of path — and the steeper bit afterwards is where they climbed a hill.

This is a common misconception

This is the big one to unlearn: the graph is not a picture of the path. The side axis is distance travelled, not height above the ground. A hiker on a steep hill and a hiker on a flat field can draw exactly the same line if they cover the same distance in the same time.

Walking at a steady speed — a flat line means the speed isn't changing.

This is a common misconception

That would only be true if the side axis showed speed. Here it shows distance. If the distance isn't changing, the hiker isn't getting anywhere. A steady speed on a distance/time graph looks like a straight line that slopes upwards.

Covering a lot of ground — the line goes a long way across the page.

This is a common misconception

Across the page is time, not distance. A long flat stretch just means a lot of time went by. To see how far the hiker went, look up the side axis — and during the flat part, that number doesn't budge.

Standing still — the minutes kept ticking by, but the distance didn't go up at all.

This matches the evidence

Exactly. Time moves on along the bottom, but the distance stays the same, so the hiker stayed in one place for those 10 minutes. The speed during that section is zero.

A distance/time graph records how far against when — it is not a map of the ground. Flat means the distance isn't growing, so the object has stopped.

Turning steepness into a speed

Problem

Go back to Jo's ride at the top of the page. What was Jo's speed between 50 s and 75 s?

Find the line where the answer goes wrong

A cyclist's distance/time graph has a straight section from (40 s, 100 m) to (60 s, 300 m). Calculate the cyclist's speed during this section.

A student's answer — which line goes wrong?

The section is a straight line, so the speed is steady and equals the gradient.
At the end of the section the cyclist has travelled 300 m after 60 s.
speed = 300 m ÷ 60 s
speed = 5 m/s

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Read a whole journey from one line — and find the speed from its slope.

What you need to know

Distance travelled goes up the side and time goes along the bottom, so the line shows how far the object has gone at every moment.
A horizontal (flat) line means the distance is not changing: the object is stationary and its speed is zero.
A straight sloping line means a steady speed, and the steeper the line, the faster the object is moving.
The gradient of a straight section is the speed: change in distance ÷ change in time, read between two points on that section.

The big picture

A distance/time graph is a record of a journey: distance travelled goes up the side and time goes along the bottom. Where the line is flat, time is passing but the distance isn't changing, so the object is stationary. Where the line slopes upwards the object is moving, and the steeper the slope, the faster it is going. The gradient of a straight section is the speed: the change in distance divided by the change in time.

Key points

1Flat line = stationary (speed 0).

2Steeper line = faster.

3Equally steep sections = equal speeds, however high up the graph they sit.

4Gradient of a straight section = speed.

5Use changes, not single readings: (later distance − earlier distance) ÷ (later time − earlier time).

6Metres ÷ seconds gives a speed in m/s.

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Worked example

Problem

A runner's distance/time graph has three straight sections. A goes from (0 s, 0 m) to (20 s, 80 m). B goes from (20 s, 80 m) to (50 s, 80 m). C goes from (50 s, 80 m) to (60 s, 140 m). Which section is the fastest, and what is the runner's speed on it?

⚠ Watch out

On a section that doesn't start at the origin, dividing one distance reading by one time reading. The speed comes from the CHANGE in distance ÷ the CHANGE in time.

🧠

Memory hook

Flat is the pause button; steep is fast-forward. The gradient tells you how fast the film is playing.

✓

Check yourself

Section P of a distance/time graph rises 60 m in 20 s. Section Q rises 60 m in 30 s. Which section is steeper, and which one shows the faster speed?

Flashcards

(6)

What does a horizontal line on a distance/time graph mean?

The object is stationary. Time passes but the distance doesn't change, so the speed is zero.

How can you spot the fastest part of a journey on a distance/time graph?

Find the steepest section — it gains the most distance each second.

What does the gradient of a distance/time graph represent?

The speed of the object.

How do you work out the gradient of a straight section?

Choose two points on the section, then divide the change in distance by the change in time.

Two sections of a distance/time graph are equally steep, but one is much higher up. How do their speeds compare?

They are the same. Height only shows how far the object has gone so far; steepness shows the speed.

Is a distance/time graph a picture of the route?

No. It plots distance against time, so a flat line means stopped, not flat ground, and a slope means moving, not going uphill.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Follow Jo's scooter ride

What does a flat line really mean?

Find the line where the answer goes wrong

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