A distance–time graph plots the distance an object has travelled from its starting point (y-axis) against time (x-axis). The gradient — steepness — of the line equals the object's speed. A steeper line means faster movement; a horizontal line means the object is stationary; a straight line means constant speed.
What does each feature of a distance–time graph mean?
Before calculating anything, predict what the graph shows:
| Feature | What it means |
|---|---|
| Straight line sloping upward | Constant speed moving away from start |
| Horizontal line | Stationary (speed = 0) |
| Steeper upward slope | Faster speed |
| Straight line sloping downward | Constant speed returning toward start |
| Curved line (slope increasing) | Accelerating (speed increasing) |
| Curved line (slope decreasing) | Decelerating (speed decreasing) |
The y-axis shows distance from the starting point — not the total distance travelled. If an object travels 10 m out and 10 m back, it ends at 0 m on the y-axis, not 20 m.
How do you calculate speed from the gradient of a distance–time graph?
Speed = distance ÷ time. On a distance–time graph, this is equivalent to:
Speed = gradient = vertical change (Δd) ÷ horizontal change (Δt)
To find the gradient of a straight-line section:
- Choose two clearly identifiable points on the line, as far apart as possible (to minimise reading error).
- Draw a right-angled triangle by dropping a vertical line from the upper point and a horizontal line from the lower point.
- Read off the vertical change in distance (Δd) and the horizontal change in time (Δt).
- Calculate: speed = Δd ÷ Δt.
Worked example 1:
A straight line goes from (0 s, 0 m) to (30 s, 150 m).
Δd = 150 − 0 = 150 m Δt = 30 − 0 = 30 s Speed = 150 ÷ 30 = 5 m/s
Worked example 2:
A line goes from (10 s, 20 m) to (50 s, 100 m).
Δd = 100 − 20 = 80 m Δt = 50 − 10 = 40 s Speed = 80 ÷ 40 = 2 m/s
How do you describe a journey from a distance–time graph?
A typical exam question shows a multi-section graph and asks you to describe the journey. Use this structure for each section: identify the time interval, state whether stationary or moving, give the direction (away from/back toward start), and state the speed.
Worked example — describing a three-section journey:
| Section | Time | Distance | Description |
|---|---|---|---|
| A | 0–20 s | 0 to 80 m | Moving away from start at 4 m/s |
| B | 20–35 s | 80 m (constant) | Stationary for 15 s |
| C | 35–55 s | 80 to 0 m | Returning toward start at 4 m/s |
The speed in section A: Δd = 80 m, Δt = 20 s → speed = 80 ÷ 20 = 4 m/s The speed in section C: Δd = 80 m, Δt = 20 s → speed = 80 ÷ 20 = 4 m/s Note that section C has the same gradient magnitude as section A, but the line slopes downward — the object is returning.
What is the difference between a distance–time graph and a velocity–time graph?
Students often confuse these two graph types:
| Feature | Distance–time graph | Velocity–time graph |
|---|---|---|
| y-axis | Distance from start (m) | Velocity or speed (m/s) |
| x-axis | Time (s) | Time (s) |
| Gradient tells you | Speed (m/s) | Acceleration (m/s²) |
| Area under the graph tells you | — | Distance travelled |
| Horizontal line means | Stationary | Constant speed |
| Upward slope means | Moving away from start | Accelerating |
The crucial point: on a distance–time graph, the gradient gives you speed. On a velocity–time graph, the gradient gives you acceleration and the area under the graph gives you distance.
How do you compare the speeds of two objects on the same graph?
When two journeys are shown on the same distance–time axes, the steeper line corresponds to the faster speed. If the lines have identical gradients (are parallel), the objects are travelling at the same speed. If the lines cross, one object has overtaken the other at that point in time.
Predict before you calculate: before working out the gradient, look at the graph and predict which section or which object is fastest based on the steepness of the lines. Then check by calculating the gradient.
Frequently asked questions
What does a horizontal line mean on a distance–time graph?
A horizontal line means the distance from the start is not changing — the object is stationary. The gradient of a horizontal line is zero, which means speed = 0 m/s. A common mistake is to say the object is at zero distance; it may be stationary anywhere along the y-axis, not necessarily at the origin. What matters is that the distance is not increasing or decreasing during that time interval.
Can the line on a distance–time graph go below the x-axis?
In most KS3 examples, distance is plotted as a positive value and the line stays above the x-axis. However, if displacement (which includes direction) is plotted instead of distance, the line can go below the x-axis — for example, if an object moves behind its starting point. At KS3, the distinction between distance and displacement is introduced but most graphs show distance from start, so the line typically stays at or above zero.
How do you find speed from a curved section of a distance–time graph?
A curved section means the speed is changing (the object is accelerating or decelerating). To find the instantaneous speed at a specific point on a curve, draw a tangent to the curve at that point — a straight line that just touches the curve without crossing it — and then calculate the gradient of that tangent. This technique is covered more fully at GCSE; at KS3, curved lines are usually identified and described qualitatively rather than calculated numerically.
Why is the gradient of a distance–time graph equal to speed?
Speed is defined as the rate of change of distance with time: speed = Δd ÷ Δt. On any graph, the gradient is defined as vertical change ÷ horizontal change = Δy ÷ Δx. On a distance–time graph, the vertical axis is distance (d) and the horizontal axis is time (t), so the gradient = Δd ÷ Δt — which is exactly the definition of speed. This is why reading the gradient directly gives you the speed, without needing any additional calculation beyond the gradient itself.
For Socratic KS3 physics with Professor Newton — predict what the graph looks like before you draw it, then check your reasoning — visit aitutors.me.