## How to calculate acceleration from a velocity-time graph

How to find acceleration from velocity-time graph data

Acceleration is the rate of change in an object’s velocity (speed in a given direction) over time. The formula to calculate acceleration is:

*Acceleration = change in velocity ÷ time taken*

To calculate acceleration from a velocity-time graph, work out the gradient of the line at a chosen point. This will always be equal to the acceleration of the object, with a positive gradient showing positive acceleration and a negative gradient signifying negative acceleration.

This is one of the many useful skills students learn during their secondary school maths education. The theory and practices involved in this topic can help to strengthen understanding of other areas of maths, such as geometry, as well as other subjects, such as physics.

In this article, we’ll focus on calculating acceleration when provided with data about velocity and time, and how graphs can make this task significantly clearer and easier.

## How to find constant acceleration from velocity

Acceleration is measured in metres per second squared (m/s^{2}). It can be calculated when you know an object’s initial velocity (u), final velocity (v) and time taken (t), where velocity is measured in metres per second (m/s) and time in seconds (s).

The formula to calculate acceleration is often presented as:

Let’s take a simple example of a car accelerating constantly from a stationary position (meaning u = 0 m/s) to a final velocity of 30 m/s in 10 s. If you were asked to determine the acceleration of the car, you could use the following calculation:

It’s important for students to grasp the underlying theory and formulae involved in determining acceleration from velocity and time, and to be able to apply this knowledge when presented with different scenarios and types of questions.

As the questions and data involved become more complex, it’s beneficial to have access to an approved GCSE calculator to ensure accuracy and check your work.

## Velocity-time graphs

Velocity-time graphs provide a clear and easily understandable way to determine acceleration. With time on the x axis and velocity on the y axis, you can add the data you have and plot a graph that shows trends and changes in acceleration.

### Determining acceleration through gradients

When looking at a velocity-time graph, the gradient of the line plotted on the graph is representative of acceleration.

On the graph above, the green line shows an object accelerating away from a stationary position to a velocity of 8 m/s in 4 s. Acceleration is therefore 2 m/s^{2}, which can be worked out either by using the a = v-ut formula, or by calculating the gradient of the line.

The object then travels in the same direction at a constant velocity of 8 m/s for 3 s, and so is not accelerating, hence the horizontal section of the graph with gradient 0, then negatively accelerates in the same direction for 3 s to a stationary position.

As you explore this and other topics in more depth over the course of your secondary education, you’ll have more to gain from the full power and functionality of a good calculator.

Explore Casio’s full range of scientific and graphic calculators for students.

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