Distance–Time and Speed–Time Graphs
Two graphs that look similar and mean completely different things. Which graph you are reading determines what the gradient and the area tell you — and confusing the two was the single largest source of recorded errors in this topic.
1. The master table
Check the y-axis label before you read anything.
| Feature | Distance–time graph | Speed–time graph |
|---|---|---|
| Gradient | speed | acceleration |
| Area under it | nothing meaningful | distance travelled |
| Horizontal line | stationary (at rest) | constant speed |
| Straight sloping line | constant speed | constant acceleration |
| Steeper line | faster | accelerating harder |
| Curve | changing speed | changing acceleration |
| Line sloping down | returning to start | decelerating |
A horizontal line means STATIONARY on a distance–time graph, but CONSTANT SPEED on a speed–time graph. This exact confusion was recorded repeatedly in both directions, and it inverts the entire interpretation of the motion. It is worth learning as a single fact.
The height of a speed–time graph is the SPEED, not the distance. Reading a value off the y-axis and calling it a distance was a specific recorded error. Distance is the area.
2. Distance–time graphs
Gradient = speed
To find the speed: pick two clear points on the straight section and calculate
speed = change in distance ÷ change in time
Example: the line goes from (2 s, 10 m) to (6 s, 50 m).
- speed = (50 − 10) ÷ (6 − 2) = 40 ÷ 4 = 10 m/s
Reading the shape:
- Horizontal → stationary
- Straight slope → constant speed
- Curve getting steeper → accelerating
- Curve getting shallower → decelerating
- Sloping down towards zero → travelling back to the starting point
A line sloping downwards on a distance–time graph does NOT mean deceleration. It means the object is moving back towards the start. Deceleration is a speed–time idea — this mix-up was recorded directly.
3. Speed–time graphs
Gradient = acceleration
acceleration = change in speed ÷ time taken, in m/s²
Example: speed rises from 5 m/s to 25 m/s in 4 s.
- a = (25 − 5) ÷ 4 = 5 m/s²
Subtract in the right order: final − initial. Reversing it gives the wrong sign, which was a recorded error. A negative gradient means deceleration — that is the correct and expected result, not a mistake.
A horizontal line means constant speed — and therefore ZERO acceleration, not zero speed. “Constant speed” and “at rest” are different states, and both confusions appeared in lessons.
Area under the graph = distance
The area between the line and the time axis is the DISTANCE travelled.
This is the most-tested idea on the page, and the one most often forgotten.
Split the area into rectangles and triangles:
- Rectangle (constant speed): distance = speed × time
- Triangle (uniform acceleration from rest): distance = ½ × base × height
- Trapezium: ½ (a + b) × h
Worked example. A car accelerates from rest to 20 m/s in 10 s, travels at 20 m/s for 30 s, then decelerates to rest in 10 s.
- Triangle 1: ½ × 10 × 20 = 100 m
- Rectangle: 20 × 30 = 600 m
- Triangle 2: ½ × 10 × 20 = 100 m
- Total distance = 800 m
Use the right shape. Treating an accelerating section as a rectangle instead of a triangle was a specific recorded error, and it doubles that part of the answer.
You cannot use “distance = speed × time” for a section where the speed is changing. That formula only works for the flat (constant-speed) parts. For accelerating sections you must take the area.
Check the axis scales before calculating an area. Misreading the scale was recorded, and one squares-based slip changes everything downstream.
4. Curved graphs and tangents
When a speed–time graph is curved, the acceleration is changing.
To find the acceleration at one instant, draw a tangent at that point and find its gradient.
Use a ruler and take two widely spaced points on the tangent. A short tangent gives a poor value. Read the coordinates from the tangent line, not from the curve.
To find the distance under a curve, count the squares (working out what one square represents) or split it into approximate triangles and trapezia. The answer is an estimate — say so.
A tangent is a straight line touching the curve, not the curve’s own shape. One recorded error was confusing the tangent with the curve.
5. Describing motion in words
Questions often ask you to describe the motion rather than calculate.
A good description names each stage with its evidence:
“From 0 to 10 s the car accelerates uniformly from rest to 20 m/s, shown by the straight positive gradient. From 10 to 40 s it travels at a constant 20 m/s, shown by the horizontal line. From 40 to 50 s it decelerates uniformly to rest.”
“Describe” means describe — don’t just calculate. A recorded error was a student computing numbers when the question asked for a description. Use the words accelerating, constant speed, decelerating, stationary, and say uniformly when the line is straight.
“Uniform” means constant, not stationary. Both “uniform velocity = no motion” and “uniform motion = accelerating” were recorded. Uniform acceleration = a straight sloping line on a speed–time graph; uniform velocity = a horizontal one.
6. Related calculations
average speed = total distance ÷ total time
Include any stationary periods in the total time.
Convert units first. Minutes must become seconds for m/s, or hours for km/h. Failing to convert was recorded, as was misreading km for m.
Echo questions: sound travels there and back, so the distance to the surface is half the total distance calculated from the time.
7. Mistakes that cost marks
Not checking which graph you’re reading.
Reading a horizontal line as stationary on a speed–time graph (it’s constant speed) — or as constant speed on a distance–time graph (it’s stationary).
Taking the height of a speed–time graph as a distance.
Forgetting that the area gives distance.
Using a rectangle where the section is a triangle.
Using distance = speed × time on an accelerating section.
Subtracting in the wrong order when finding a gradient.
Treating a downward slope on a distance–time graph as deceleration.
Drawing a tangent freehand, or too short.
Reading tangent coordinates off the curve.
Misreading the axis scales.
Calculating when the question said “describe”.
Forgetting to halve the distance in an echo question.
Not converting time units.
Frequently asked questions
What does the gradient of a distance–time graph show? The speed.
What does the gradient of a speed–time graph show? The acceleration.
What does the area under a speed–time graph show? The distance travelled.
What does a horizontal line mean? Stationary on a distance–time graph; constant speed on a speed–time graph.
How do I find the distance from a speed–time graph? Find the area — split it into rectangles, triangles and trapezia.
What does a negative gradient on a speed–time graph mean? Deceleration.
What does a downward slope on a distance–time graph mean? The object is moving back towards its starting point.
How do I find acceleration at one instant on a curve? Draw a tangent and find its gradient.
What are the units of acceleration? m/s².
What does “uniform acceleration” mean? Constant acceleration — a straight sloping line on a speed–time graph.
Quick revision checklist
- I check the y-axis before interpreting any motion graph
- I know gradient = speed on a distance–time graph
- I know gradient = acceleration on a speed–time graph
- I know area = distance on a speed–time graph
- I know what a horizontal line means on each graph
- I can calculate a gradient, subtracting final − initial
- I know a negative gradient means deceleration
- I can split an area into rectangles, triangles and trapezia
- I don’t use speed × time on accelerating sections
- I can draw a tangent with a ruler to find instantaneous acceleration
- I can estimate the area under a curve
- I can describe motion in the right words, stage by stage
- I can find average speed including stopped time
- I convert time units and halve echo distances
These notes cover distance–time and speed–time graphs in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
Finished this topic?
Saved on this device — no account needed.