---
title: "Acceleration from Velocity-Time Graphs"
description: "Read acceleration from the gradient of a velocity-time graph. Signed area gives displacement; adding the magnitudes of areas gives distance travelled. Interpret positive and negative gradients using t"
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: 2026-11-12
---

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# Acceleration from Velocity-Time Graphs

Read acceleration from the gradient of a velocity-time graph. Signed area gives displacement; adding the magnitudes of areas gives distance travelled. Interpret positive and negative gradients using the sign of velocity, since a negative gradient does not always mean 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 displacement from signed areas and distance travelled from the magnitudes of areas on 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 velocity-time graphs

Acceleration is velocity change per time. Average acceleration = (final velocity - initial velocity) ÷ elapsed time, in m/s². From rest to 12 m/s in 4 s gives 3 m/s². On a straight velocity-time section, this is its constant gradient.

Plot time horizontally and signed velocity vertically. Gradient gives acceleration. A flat line means constant velocity, including rest at zero. A downward slope above zero shows slowing; below zero it shows increasing speed in the negative direction.

**Example.** Split area into rectangles and triangles, splitting again at zero crossings. Rectangle size = time width × nonnegative velocity height; 8 m/s for 5 s gives 40 m. Triangle size = half × width × nonnegative height, using the magnitude of the velocity difference. For displacement, count below-axis areas negatively. For distance, add all area sizes positively.

Here distance means total distance travelled, not distance from the start. Returning still adds distance. A distance-time gradient gives speed. For constant positive acceleration from rest, distance-time curves upward and gets steeper; velocity-time rises straight. At constant positive velocity, distance-time rises straight and velocity-time is flat. Total distance travelled never decreases.

**Recap.** Gradient gives acceleration. Signed area gives displacement; adding area sizes gives distance. Check velocity's sign before deciding whether speed rises or falls.

*Lesson, questions and flashcards written for this dataset.*

## 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)