---
title: "Acceleration from Velocity-Time Graphs"
description: "Reading a velocity-time graph two ways: the gradient gives the acceleration, and the area under the line gives the distance travelled. A negative gradient shows slowing down."
canonical: https://lightmysky.com/learn/science/acceleration-from-velocity-time-graphs-mt_nmvfbSgnOn
source: https://lightmysky.com/learn/science/acceleration-from-velocity-time-graphs-mt_nmvfbSgnOn.md
retrieved: 2026-09-12
---

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# Acceleration from Velocity-Time Graphs

Reading a velocity-time graph two ways: the gradient gives the acceleration, and the area under the line gives the distance travelled. A negative gradient shows slowing down.

Subject: Science · Area: Forces & Motion · Ages 14 to 15
Page: https://lightmysky.com/learn/science/acceleration-from-velocity-time-graphs-mt_nmvfbSgnOn

## Ready when they can

- Calculates acceleration as a gradient and quotes it in metres per second squared
- Finds distance travelled from the area under a velocity-time graph made of straight sections
- Sketches the distance-time graph and the velocity-time graph of the same journey and says how they differ

## Lesson: Reading speed from a graph

Acceleration tells you how fast velocity changes. A car going from rest to 20 metres per second in 5 seconds has acceleration 4 metres per second squared. Slowing down counts too, pointing the opposite way to the motion.

On a velocity-time graph, acceleration is the steepness of the line. A steep upward slope means big acceleration, a flat line means steady speed with zero acceleration, and a downward slope means the object is slowing down.

**Example.** The area under the line equals the distance travelled. If the graph is made of straight sections, split the area into rectangles and triangles, work out each chunk, then add them up. Try it: 10 metres per second for 6 seconds is a rectangle of 60 metres.

**Tip.** Motion graphs come in pairs telling one story two ways. For steady speeding up, the distance-time graph curves upward while the velocity-time graph is a straight rising slope. Always finish by asking if your answer makes sense on the graph.

**Recap.** Read acceleration from the slope and distance from the area.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Vectors, Scalars and Free-Body Diagrams](https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1)
- [Speed & Distance-Time Graphs](https://lightmysky.com/learn/science/speed-and-distance-time-graphs-mt_q-1a86ydgU)

## Opens up

- [Combining Uncertainties and Reading a Result off a Graph](https://lightmysky.com/learn/science/combining-uncertainties-and-reading-a-result-off-a-graph-mt_kn8RhTDEOK)
- [The Uniform Acceleration Equations](https://lightmysky.com/learn/science/the-uniform-acceleration-equations-mt_yJMJQ8_KqR)