# Velocity-Time Graphs

## Description

This is a simple physics tutorial aimed at high school students in grades 9 and 10 (GCSE, HSC) exploring velocity-time graphs.

## Introduction

We've learned that the acceleration of an object is its change in velocity over time:

## What are Velocity-Time graphs?

Velocity-time graphs are a way of representing a journey in a graph, typically with the y-axis representing velocity, and the x-axis representing time.

## Calculating Acceleration from Velocity-Time Graphs

Importantly the gradient or slope of a conventional distance-time graph (y-axis = velocity, x-axis = time) is the same as average acceleration:

Hover your mouse over the graph below to see how to work out the acceleration of an object from a velocity-time graph.

If the axes of the graph are swapped (i.e. velocity on the x axis, and time on the y axis) then acceleration can be calculated by inversing the slope (as below) - hover your mouse over to see the two methods of calculating acceleration.

Method 1 involves reading values off the graph for change in velocity and time; method 2 involves calculating the slope and then inversing it to get the average acceleration.

## Benefit of Velocity-Time graphs

In addition to being able to calculate acceleration from a velocity-time graph, there two other benefits to them. They can be used to:

• compare the accelerations of different objects at a glance
• determine the displacement of an object (explored in a future tutorial)

## Comparing Accelerations using Velocity-Time Graphs

Velocity-time graphs are particularly useful because they make it easy to compare the acceleration of one object to another at a glance i.e. without having to do any calculations. Knowing what you know now, look at the below graph and work out which of the three lines depicted represents the journey with the fastest and slowest average acceleration; then mouse over the image for the answer.

## Exercise Worksheet

Below is the follow on worksheet for this tutorial. It has two sample calculations so that you can see what you need to do to calculate the acceleration of different objects. To download the worksheet, visit Slideshare here: