What you'll learn
Real-life graphs represent practical situations such as journeys, conversions and rates. In this guide you will learn how to read and interpret distance–time and speed–time graphs, how to find speeds and accelerations from gradients, how to interpret conversion and other real-life graphs, and how to relate graph features to the situation they describe. These skills appear in functional and interpretation questions at GCSE.
Key terms and definitions
Distance–time graph — a graph of distance against time; its gradient is speed.
Speed–time (velocity–time) graph — a graph of speed against time; its gradient is acceleration and the area under it is distance.
Gradient — the steepness of the graph, representing a rate.
Conversion graph — a straight-line graph used to convert between two units.
Rate — how one quantity changes with respect to another.
Core concepts
Distance–time graphs
On a distance–time graph, the gradient represents speed (distance ÷ time). A steeper line means a faster speed; a horizontal line means the object is stationary (no change in distance); a line returning towards the start means moving back. A straight sloping line means constant speed.
Finding speed from a distance–time graph
The speed for a section is the gradient = change in distance ÷ change in time. For a curved distance–time graph, the speed is changing, and the gradient of a tangent gives the speed at an instant.
Speed–time graphs
On a speed–time graph, the gradient represents acceleration (change in speed ÷ time). A positive gradient means accelerating, a negative gradient means decelerating, and a horizontal line means constant speed. The area under the graph gives the distance travelled.
Finding distance from a speed–time graph
The distance travelled equals the area under the speed–time graph. Split the area into rectangles, triangles and trapeziums, calculate each, and add them. This is a common higher-mark question.
Conversion and other real-life graphs
A conversion graph is a straight line used to convert between units (e.g. miles and kilometres, pounds and dollars). Read across and up to convert a value. Other real-life graphs (e.g. cost against quantity, or filling a container) can be interpreted by relating the gradient and shape to the situation.
Worked examples
Example 1: Speed from distance–time
An object travels 60 m in 12 s at constant speed. What is its speed?
Speed = gradient = 60 ÷ 12 = 5 m/s.
Example 2: Acceleration from speed–time
Speed rises from 0 to 20 m/s in 8 s. Find the acceleration.
Acceleration = gradient = (20 − 0) ÷ 8 = 2.5 m/s².
Example 3: Distance from speed–time
An object travels at a constant 15 m/s for 10 s. What distance is shown on the graph?
Area = 15 × 10 = 150 m.
Common mistakes and how to avoid them
Confusing the two graph types. Distance–time gradient = speed; speed–time gradient = acceleration.
Forgetting area = distance on a speed–time graph.
Misreading a horizontal line. On a distance–time graph it means stationary, not constant speed.
Reading conversion graphs the wrong way. Go across to the line, then up or down to the other axis.
Errors splitting areas. Break complex areas into simple shapes carefully.
Exam technique for Real-life Graphs
Identify the graph type before interpreting.
Use the gradient for speed (distance–time) or acceleration (speed–time).
Find distance from the area under a speed–time graph.
Read conversion graphs by going to the line and across.
Relate features to the situation — stationary, accelerating, constant.
Quick revision summary
Real-life graphs model practical situations. On a distance–time graph, the gradient is speed — steeper means faster, a horizontal line means stationary, and the gradient of a tangent gives the speed at an instant on a curve. On a speed–time graph, the gradient is acceleration (positive = accelerating, negative = decelerating, horizontal = constant speed) and the area under the graph is the distance travelled, found by splitting into rectangles, triangles and trapeziums. Conversion graphs are straight lines for changing units — read across to the line and then to the other axis. Other real-life graphs are interpreted by relating their gradient and shape to the situation. The common errors are confusing the two graph types, forgetting that area gives distance, misreading horizontal lines, and reading conversion graphs incorrectly. Identify the graph type, use the gradient for the right rate, use area for distance on speed–time graphs, and connect every feature back to what is physically happening.