# Velocity-time graph

A graph of velocity against time. The gradient is the acceleration. The area under the line is the distance travelled.

Physics (school) · Part 01: Motion and measurement · Card 7 of 8 · Last updated 2026-10-19

## Analogy

The slope is how hard you press the pedal. The area is how far you have got.

## Example

**Reading both**

Line from (0 s, 0 m/s) to (3 s, 6 m/s).
acceleration = 6 / 3 = 2 m/s squared
distance = area of triangle
= 0.5 x 3 x 6 = 9 m

## In practice

Engineers use it to check how far a train travels while speeding up.

## Practice

### Flashcards

- **What does the area under a velocity-time graph give?** The distance travelled.

### Interview questions

**A train speeds up steadily from 5 m/s to 25 m/s in 10 s. Calculate its acceleration and the distance it covers in that time.**

- Acceleration = (25 - 5) / 10 = 2 m/s squared
- Average velocity = (5 + 25) / 2 = 15 m/s
- Distance = 15 x 10 = 150 m
- Give units with each answer

## Questions people ask

### What does the area under a velocity-time graph show?

The area is the distance travelled. Split the shape into rectangles and triangles, work out each area, and add them up. Velocity multiplied by time gives distance, and that is exactly what each little slice of area represents on the graph.

### What does a horizontal line on a velocity-time graph mean?

The velocity is not changing, so the acceleration is zero. The object is moving at a steady speed in a straight line. This is different from a horizontal line on a distance-time graph, which means the object is standing still.

## Related concepts

- [Acceleration](https://studyvisually.com/learn/science/physics-school/physics-school-part-1/physics-school-part-1-concept-6)
- [Distance-time graph](https://studyvisually.com/learn/science/physics-school/physics-school-part-1/physics-school-part-1-concept-5)
- [Speed](https://studyvisually.com/learn/science/physics-school/physics-school-part-1/physics-school-part-1-concept-3)
- [Velocity](https://studyvisually.com/learn/science/physics-school/physics-school-part-1/physics-school-part-1-concept-4)

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