Velocity-time graphs GCSE physics questions test two skills: reading the gradient to find acceleration in m/s², and reading the area under the line to find distance travelled in metres. A line sloping upward means speeding up, sloping downward means slowing down, and a flat line means constant velocity — combine both readings to answer any exam question.
What does a velocity-time graph show?
A velocity-time graph plots velocity (usually in m/s) on the vertical axis against time (in seconds) on the horizontal axis. Unlike a distance-time graph, which tells you how far an object has travelled, a velocity-time graph tells you how an object's speed is changing over time — and because the area under the line represents distance, it also lets you calculate how far the object travelled without needing a separate graph.
Three line shapes to recognise immediately:
- A horizontal line means constant velocity — the object is neither speeding up nor slowing down, so acceleration is zero.
- A straight line sloping upward means constant (uniform) acceleration — the velocity increases by the same amount every second.
- A straight line sloping downward means constant deceleration — the object slows down at a steady rate.
A curved line means the acceleration itself is changing, but GCSE questions almost always use straight-line sections, which keeps the maths to straightforward gradient and area calculations.
How do you read a velocity-time graph step by step?
Work through any velocity-time graph question using the same method every time:
- Label the axes and check the units — velocity is usually in m/s, time in seconds.
- Split the graph into straight-line sections wherever the slope changes.
- For each section, calculate the gradient to find the acceleration during that phase.
- For each section, calculate the area under the line to find the distance travelled during that phase.
- Add the distances from every section together to find the total distance travelled.
This five-step method works for any combination of accelerating, constant-velocity, and decelerating sections — including the classic trapezium-shaped journey graph that appears throughout GCSE physics papers.
How do you find the gradient of a velocity-time graph?
The gradient of a velocity-time graph equals the acceleration. Choose two clear points on a straight section, then use:
gradient = acceleration (m/s²) = change in velocity (m/s) ÷ change in time (s)
If the line rises, acceleration is positive (speeding up). If it falls, acceleration is negative (decelerating). A horizontal line has a gradient of zero, meaning zero acceleration.
Worked example: A cyclist's velocity increases in a straight line from 2 m/s to 14 m/s over 4 seconds. What is the acceleration?
- Change in velocity = 14 − 2 = 12 m/s
- Change in time = 4 s
- Acceleration = 12 ÷ 4 = 3 m/s²
How do you find the area under a velocity-time graph?
The area between the line and the time axis equals the distance travelled. For straight-line sections, the shape underneath is usually a rectangle, a triangle, or a trapezium — all of which use GCSE-level area formulas.
| Shape under the line | When it appears | Area formula |
|---|---|---|
| Rectangle | Constant velocity | length × height |
| Triangle | Starts from, or returns to, zero velocity | ½ × base × height |
| Trapezium | Section starts and ends at different non-zero velocities | ½ × (sum of parallel sides) × height |
Worked example: reading a full velocity-time graph
A car's motion over 18 seconds is shown by a velocity-time graph with three straight sections:
- 0–5 s: velocity increases steadily from 0 m/s to 15 m/s.
- 5–15 s: velocity stays constant at 15 m/s.
- 15–18 s: velocity decreases steadily from 15 m/s to 0 m/s.
| Section | Gradient (acceleration) | Shape under line | Area (distance) |
|---|---|---|---|
| 0–5 s | (15 − 0) ÷ 5 = 3 m/s² | Triangle | ½ × 5 × 15 = 37.5 m |
| 5–15 s | 0 m/s² | Rectangle | 10 × 15 = 150 m |
| 15–18 s | (0 − 15) ÷ 3 = −5 m/s² | Triangle | ½ × 3 × 15 = 22.5 m |
Total distance travelled = 37.5 + 150 + 22.5 = 210 metres over the full 18 seconds.
Notice that the steepest section (0–5 s) has the greatest acceleration, while the flat section (5–15 s) contributes the largest single share of the total distance simply because it lasts the longest at the highest velocity.
How are velocity-time graphs different from distance-time graphs?
Students frequently mix up what the gradient and area mean on each graph type. Compare them directly:
| Feature | Distance-time graph | Velocity-time graph |
|---|---|---|
| y-axis | Distance (m) | Velocity (m/s) |
| Gradient tells you | Speed (m/s) | Acceleration (m/s²) |
| Area under the line | Not a meaningful quantity | Distance travelled (m) |
| Horizontal line means | Stationary object | Constant velocity |
| Straight sloping line means | Constant speed | Constant acceleration |
The key rule: on a distance-time graph, only the gradient is useful. On a velocity-time graph, both the gradient (acceleration) and the area (distance) give real physical information — which is why exam questions favour velocity-time graphs when they want to test both ideas at once.
Frequently asked questions
What does the gradient of a velocity-time graph represent?
The gradient represents acceleration, measured in m/s². It is calculated as the change in velocity divided by the change in time between two points on a straight section of the line. A steeper gradient means a greater acceleration; a negative gradient means the object is decelerating.
What does the area under a velocity-time graph represent?
The area between the line and the time axis represents the distance travelled, measured in metres. For straight-line sections this area is usually a rectangle, triangle, or trapezium, and the areas of each section can be added together to find the total distance for the whole journey.
How do you know if a velocity-time graph shows acceleration or constant speed?
A horizontal line shows constant velocity, meaning zero acceleration. A straight line sloping upward shows constant acceleration — the object is speeding up at a steady rate. A straight line sloping downward shows constant deceleration. Only a curved line shows changing acceleration, which is rare in GCSE-level questions.
What is the difference between distance-time graphs and velocity-time graphs?
A distance-time graph plots distance against time, and its gradient gives speed. A velocity-time graph plots velocity against time; its gradient gives acceleration and the area under the line gives distance travelled. Confusing the two — reading a distance-time gradient as if it were acceleration, for example — is one of the most common GCSE physics exam mistakes.
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