GCSE · Physics · AQA · Spec 8463

Distance–time graphs

Read a graph line and you can tell exactly how fast something moved — no stopwatch needed.

What you need to know

  • A straight sloping line on a distance–time graph means constant speed; gradient = speed.
  • A horizontal line means the object is stationary — distance is not changing.
  • A curve on the graph means the speed is changing — the object is accelerating or decelerating.
  • Higher tier: find the speed at a specific instant on a curve by drawing a tangent at that point and calculating its gradient.

The big picture

A distance–time graph shows how far an object has travelled over time. The steeper the line, the faster the object is moving — gradient equals speed. A flat horizontal line means the object is stationary. A curve means the speed is changing (the object is accelerating or decelerating).

TONIGHT'S REVISION

Distance–time graphs

How to read gradient as speed — and spot acceleration from a curve.

Maths & Science · Interpret graphs

Reading a distance–time graph

Use the gradient tools to extract speed from each section of the journey.

A distance–time graph
020406080024681012Time (s)Distance (m)riserun
Gradient at t = 4s
≈ 12.5 m/s
Steepness of the tangent. On a distance–time graph, gradient = speed at that instant.
Gradient. The tangent’s steepness tells you the speed at one moment.

Selected tool

Gradient

Reading

Gradient at t = 4s

Value

≈ 12.5 m/s

Steepness of the tangent. On a distance–time graph, gradient = speed at that instant.

Exam line: Always show your gradient triangle on the graph with rise and run values labelled — examiners must see the working to award the method mark.
Watch out: A steep straight line means fast constant speed — it does NOT mean acceleration. Only a curve means the speed is changing.

Predict, then check

Look at each section description — commit to an answer before you reveal.

A distance–time graph has three sections: (1) a steep straight line, (2) a horizontal flat section, (3) a shallower straight line. Which section shows the object moving at its FASTEST speed?

How to find speed from a distance–time graph

Follow every step in order — this is the method examiners expect to see written down.

Relationship matrix

Tap any cell to reveal it. Tap a column header to read one property down every item.

SpeedSpeed changing?Gradient
Steep straight lineLarge gradient
Shallow straight lineSmall gradient
Horizontal lineZero gradient
Curve (getting steeper)Increasing gradient

Each cell hides a short answer and the reason behind it. Predict before you tap.

Higher

Process · Closed loop

Higher tier: Finding instantaneous speed from a curve

Use this repeatable cycle whenever the distance–time graph is curved.

1Locate the point2Place the ruler3Draw the straight line4Read rise and run5Calculate gradient

Stage 01

Locate the point

Exam line: Higher tier: The examiner must see the straight line drawn on the graph and your gradient triangle labelled — without them, you cannot earn the method marks.
Watch out: Higher tier: Do not draw a line joining two points on the curve — that gives average speed, not instantaneous speed. The line must touch the curve at exactly ONE point.

AQA Paper 2 — exam technique

AQA mark-scheme practice

Does this student answer contain the phrases that unlock marks?

Question

Describe the motion shown by the distance–time graph. Section A: steep straight line for 10 s. Section B: horizontal line for 5 s. Section C: shallower straight line for 10 s.

Student answer

In section A the object moves at constant speed. In section B the object is stationary. In section C the object moves at constant speed but more slowly than in section A.

Method marks0/3

Equations you need

Taken directly from the exam-board specification.

v = s / t

v = speed (m/s) · s = distance (m) · t = time (s)

Learn it — you must recall this in the exam

Key points

1Gradient of a distance–time graph = speed (m/s when axes are metres and seconds).
2Steeper gradient → faster speed; shallower gradient → slower speed.
3Flat (horizontal) section → object is stationary, speed = 0.
4Curved section → speed is changing; the object is accelerating or decelerating.
5Higher tier: draw a tangent to the curve at a point to find the instantaneous speed at that moment.

Worked example

Problem

A cyclist travels 600 m in 40 s at constant speed. What is the cyclist's speed? Show how you would read this from a distance–time graph.

🧠

Memory hook

STEEP = SPEEDY, FLAT = FROZEN, CURVE = CHANGING — three words that cover every line shape you will ever see on a distance–time graph.

★ Exam tip

On AQA Paper 2, always show your gradient calculation with a clearly labelled rise-and-run triangle drawn on the graph — examiners award a method mark for the working even if you misread a value. Higher tier: when drawing a tangent to a curve, extend the line as far as possible across the graph before reading off rise and run, to minimise reading errors.

⚠ Watch out

Confusing a steep straight line with acceleration — a steep straight line is FAST CONSTANT SPEED, not speeding up. Only a CURVE means the speed is changing.

✓

Check yourself

Without looking — sketch what a distance–time graph looks like for an object that travels fast, then stops, then travels slowly. What are the three key features of your sketch?

Flashcards

(22)
What does the gradient of a distance–time graph equal?
Speed — gradient = rise ÷ run = change in distance ÷ change in time.
What does a straight sloping line on a distance–time graph show?
The object is moving at constant speed.
What does a horizontal (flat) line on a distance–time graph show?
The object is stationary — its distance is not changing.
What does a curve on a distance–time graph show?
The speed is changing — the object is accelerating or decelerating.
Write the equation for speed.
v = s / t
What are the units of speed when distance is in metres and time is in seconds?
Metres per second (m/s).
A steeper gradient on a distance–time graph means what?
A greater (faster) speed.
Two objects have straight lines on the same distance–time graph. Object A has a steeper line. What does this mean?
Object A is moving faster than Object B.
Higher tier: How do you find the speed of an object at a specific instant when the distance–time graph shows a curve?
Draw a tangent to the curve at that point and calculate the gradient of the tangent line.
Higher tier: Why must you draw a tangent to find speed on a curved distance–time graph?
The gradient of the curve changes at every point; the tangent gives the gradient at one specific instant, giving the instantaneous speed.
What does a decreasing gradient on a distance–time graph tell you about the object's motion?
The speed is decreasing — the object is slowing down (decelerating).
An object's distance–time graph shows a horizontal line for 5 s. What is its speed during this time?
0 m/s — the object is stationary.
How do you calculate the gradient of a straight line on a distance–time graph?
Gradient = change in distance ÷ change in time (rise ÷ run). Pick two points far apart on the line for accuracy.
A car travels 300 m in 20 s at constant speed. What is its speed?
v = 300 ÷ 20 = 15 m/s.
What shape is the line on a distance–time graph for a uniformly accelerating object?
A curve that gets progressively steeper.
Higher tier: On a curved distance–time graph, what does a steeper tangent drawn at a later time indicate?
The instantaneous speed at that later time is greater — the object is still accelerating.
What two quantities do you need to read from the graph axes to calculate speed?
A change in distance (rise, in metres) and the corresponding change in time (run, in seconds).
Higher tier: What is meant by 'instantaneous speed' on a distance–time graph?
The speed of the object at one specific moment in time, found by the gradient of the tangent at that point on a curve.
An object's distance–time graph shows a curve that gets progressively steeper. What is happening to the object?
The object is accelerating — its speed is increasing over time.
Which AQA paper assesses distance–time graphs?
Paper 2.
A distance–time graph has gradient = 0. What does this tell you about the object?
The object is stationary — it is not moving.
If the gradient of a straight section of a distance–time graph is 12, what is the object's speed?
12 m/s.

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.

Learn Distance–time graphs properly — interactive practice, marked questions and flashcards.

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