corbettmaths travel graph

One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths revision lessons now available

In order to access this I need to be confident with:

This topic is relevant for:

Distance Time

Distance Time Graph

Here we will learn about distance-time graphs, including how to interpret and construct them.

There are also distance-time graph worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are distance time graphs?

Distance-time graphs are graphs that show the distance an object or person has travelled against time. They can also be referred to as travel graphs.

A distance-time graph will show the distance (in metres, kilometres, miles etc.) on the vertical axis ( y -axis) and the time (in seconds, minutes, hours etc.) on the horizontal axis ( x -axis).

The distance-time graphs we will look at on this page will all be drawn using straight lines.

Straight lines on a distance-time graph represent constant speeds. To find the speed from a distance-time graph you will need to be able to find the gradient of the straight lines.

The steeper the gradient , the faster the object is travelling .

One way of calculating the speed from a distance-time graph is to think about how far the object has travelled in one time unit.

For example, if an object has travelled 20 miles in 30 minutes, it would travel 40 miles in one hour, therefore the speed is 40 \ mph.

How to read distance time graphs

In order to read distance-time graphs:

Locate any relevant points from the distance-time graph.

Check the information required. For example, distance travelled at a selected time, period of being stationary, speed at a selected point in the journey.

• Use the appropriate process from the list.
• Distance travelled at a selected time – read from the vertical axis at the given time.
• Period of being stationary – find the time when the line is horizontal.
• Speed at a selected point in the journey – find the gradient of the line at that time or think how far has the object travelled in one time unit.
• Average speed for the whole journey – divide the total distance travelled by the total time.

Explain how to read distance time graphs

Distance time graph worksheet

Get your free distance time graph worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on rates of change

Distance time graph is part of our series of lessons to support revision on rates of change . You may find it helpful to start with the main rate of change lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Rate of change
• Speed time graph

Reading distance time graphs examples

Example 1: finding the distance travelled from a distance-time graph.

The distance-time graph shows the journey of a person from their home.

How far away from their home are they after 1 hour and 30 minutes?

Locate 1 hour 30 minutes on the horizontal axis and go up to the graph line.

2 Check the information required. For example, distance travelled at a selected time, period of being stationary, speed at a selected point in the journey.

We require the distance travelled at that time.

3 Use the appropriate process from the list. Distance travelled at a selected time – read from the vertical axis at the given time.

Reading from the vertical axis gives a distance of 25 \ km.

Example 2: finding stationary periods from a distance-time graph

At what time did the person first stop and for how long?

Locate the points in the graph when the line changes.

We required the first period that the person was stationary.

Use the appropriate process from the list. Period of being stationary – find the time when the line is horizontal.

The person was first stationary after 30 minutes, and remained stationary for 30 minutes.

Example 3: finding the speed from a distance-time graph  

The graph shows the person taking a bus to a cafe. They then stopped at the cafe for a drink and snack. They then ran for an hour, before taking a taxi home. 

What speed was the person travelling during the taxi journey home?

The journey home began after 2 hours 30 minutes and finished at 3 hours.

We require the speed between 2.5 hours and 3 hours.

Use the appropriate process from the list. Speed at a selected point in the journey – find the gradient of the line at that time or think how far has the object travelled in one time unit.

The person travelled 30 \ km in 30 minutes, this would mean they would travel 60 \ km in 1 hour, therefore, their speed was 60 \ km/h.

We could also find this using the speed, distance, time formula,

\text{Speed}=\frac{\text{distance}}{\text{time}}=\frac{30}{0.5}=60\,\text{km/h}

(it is important to use 0.5 hours and not 30 minutes for the time).

Or we could have found the gradient of the line,

\frac{\text{Change in }y}{\text{Change in }x}=\frac{30}{0.5}=60.

Example 4: finding the average speed of the whole journey from a distance-time graph

The graph shows the person taking a bus to a cafe. They then stopped at the cafe for a drink and snack. They then ran for an hour, before taking a taxi home.

What was the person’s average speed for their whole journey?

We need to find the total distances travelled.

We required the average speed for the whole journey.

Use the appropriate process from the list. Average speed for the whole journey – divide the total distance travelled by the total time.

It is important to add all the distances travelled and find the time for the whole journey including any periods when the person was stationary.

\text{Average speed =}\frac{\text{total distance}}{\text{total time}}=\frac{60}{3}=20 \ \text{km/h.}

How to draw distance time graphs

In order to draw distance-time graphs:

Draw/label the horizontal axis for the time and a vertical axis for the distance.

Use the information about the distance or speed of the object to plot points on the graph.

Join the points with straight line segments.

Explain how to draw distance time graphs

Drawing distance time graph examples

Example 5: drawing a distance-time graph from information about distance at given times.

A car starts from home and travels at a constant speed for 30 minutes until it is 20 miles from home. It then stops for 1 hour before returning home, travelling at a constant speed for 45 minutes.

Draw a distance-time graph to represent the journey.

The car gets no further than 20 miles from home and the journey takes a total of 2 hours 15 minutes. Draw and label the vertical axis from 0 to 20 miles and the horizontal axis from 0 to 3 hours.

The car starts at home, so plot the point (0, 0).

After 30 minutes the car has travelled 20 miles, so plot the point (0.5,20).

It remains stationary for 1 hour, so plot the point (1.5,20).

It then returns home after 45 minutes, so plot the point (2.25,0).

Example 6: drawing a distance-time graph from information about speed at given times

A car leaves home at 12 : 00 and sets off at a constant speed of 30 \ mph.

At 12 : 30 the car stops for 10 minutes. It then returns home at a speed of 45 \ mph.

Draw the horizontal and vertical axes, but we will finish labelling them once we know more information about the maximum distance and times taken based on the information provided about the speed.

Plot (12 : 00,0).

The car travels at a speed of 30 \ mph between 12 : 00 and 12 : 30. \ 30 \ mph means it would travel 15 miles in 30 minutes, so we will need to plot (12 : 30,15).

The car stops for 10 minutes, so we will need to plot (12 : 40,15).

The car returns home at a speed of 45 \ mph.

You can use \text{time =}\frac{\text{distance}}{\text{speed}}=\frac{15}{45}=\frac{1}{3} \ hour, so it will take 20 mins to travel 15 miles.

We will need to plot (13 : 00,0).

Choose appropriate scales for the axes and plot the points.

Example 7: drawing a distance-time graph from information about distance and speed at given times

A person walks from home for 10 minutes to a distance of 1 \ km. They stop for 5 minutes, and then run at a speed of 8 \ km/h away from home. After 45 minutes they immediately change direction and run towards home at a speed of 7 \ km/h.

Draw a distance-time graph to represent their journey.

The person starts from home, so we will need to plot (0, 0).

The person walks from home for 10 minutes to a distance of 1 \ km, so we will need to plot (10,1).

They stop for 5 minutes, so we will need to plot (15,1).

Then run at a speed of 8 \ km/h away from home for 45 minutes. 45 minutes = 0.75 hours. Using \text{distance = speed}\times \text{time = }8\times 0.75=6 \ km.

We will need to plot (60,7).

They immediately change direction and run towards home at a speed of 7 \ km/h, they have 7 \ km to run which will take 60 minutes, so we will need to plot (120,0)

Common misconceptions

• Confusing distance-time graphs with speed-time graphs

It is common for students to confuse distance-time graphs with speed-time graphs. This may result in students just reading a value from the vertical axis instead of calculating the gradient of a distance-time graph to find a speed.

• Calculating average speed incorrectly

The average speed could be incorrectly calculated by finding the mean of the different speeds during a journey. Another incorrect method is to only use the periods when the object is moving and to forget to include the periods when it is stationary.

• Drawing impossible distance-time graphs

There are some graphs that would be impossible for a distance-time graph. For example, vertical lines would represent an infinite speed.

Objects travelling back in time.

Practice distance time graph questions

1. A horizontal line on a distance-time graph shows that …

The object is accelerating.

The object is stationary.

The object is moving at a constant speed.

The object is decelerating.

A horizontal line shows the object is covering zero distance for a period of time.

2. Which of the distance-time graphs shows an object moving at the greatest speed?

Greater speeds have a steeper gradient.

3. What is the speed of the object shown in this distance-time graph?

The object travels 40 \ km in 2 hours.

4. What is the speed of the object shown in this distance-time graph?

The object travels 120 miles in 1.5 hours, so it must travel 80 miles in 1 hour.

5. An object travels away from home at a speed of 60 \ km/h for half an hour. It then stops and remains stationary for a quarter of an hour before returning home at a speed of 40 \ km/h. Select the correct distance-time graph for the journey.

60 \ km/h for 30 minutes gives a distance of 30 \ km. \ 0 \ km at 40 \ km/h will take 45 minutes.

6. The image shows part of a distance-time graph.

The last part of the journey is for the object to return home at a speed of 80 \ km/h. Which is the correct completed distance-time graph?

40 \ km at 80 \ km/h will take 30 minutes. The journey ends after 90 minutes.

Distance time graph GCSE questions

1. A salesperson was driving on a motorway from London to York. He stopped at a motorway service station halfway into his journey.

Which of the distance-time graphs could represent his journey?

• 2. The distance-time graph shows part of a journey Sarah took on a bike ride.

(a) What did Sarah do between 09 : 45 and 10 : 00?

(b) What was Sarah’s speed between 10 : 00 and 10 : 30, in km/h?

She stopped moving/was stationary.

Process of dividing 6 \ km by 0.5 hours or equivalent method.

3. The distance-time graph shows the first part of a journey of a person on a shopping trip.

The person walked from their home to the shop and arrived at 12 : 00.

The person stays in the shop for 15 minutes and then catches a bus home.

The bus stopped outside their door and travelled at an average speed of 20 miles per hour.

(a) At what speed did they walk to the shops? Give your answer in miles per hour.

(b) Complete the distance-time graph showing the remaining parts of their journey.

Horizontal line to (12 : 15, 5).

Process to find the time for the bus ride ( 15 minutes).

Line from (12 : 15, 5) to (12 : 30,0).

Learning checklist

You have now learned how to:

• Read and interpret distance-time graphs
• Draw distance-time graphs
• Calculate speed from distance-time graphs

The next lessons are

• Conversion graphs
• Units of measurement
• Scale maths

Still stuck?

Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.

Find out more about our GCSE maths tuition programme.

Privacy Overview

Travel Graphs

This section covers travel graphs, speed, distance, time, trapezium rule and velocity.

Speed, Distance and Time

The following is a basic but important formula which applies when speed is constant (in other words the speed doesn't change):

Remember, when using any formula, the units must all be consistent. For example speed could be measured in m/s, distance in metres and time in seconds.

If speed does change, the average (mean) speed can be calculated: Average speed = total distance travelled                              total time taken

In calculations, units must be consistent, so if the units in the question are not all the same (e.g. m/s, m and s or km/h, km and h), change the units before starting, as above.

The following is an example of how to change the units:

Change 15km/h into m/s. 15km/h = 15/60 km/min               (1) = 15/3600 km/s = 1/240 km/s      (2) = 1000/240 m/s = 4.167 m/s        (3)

In line (1), we divide by 60 because there are 60 minutes in an hour. Often people have problems working out whether they need to divide or multiply by a certain number to change the units. If you think about it, in 1 minute, the object is going to travel less distance than in an hour. So we divide by 60, not multiply to get a smaller number.

If a car travels at a speed of 10m/s for 3 minutes, how far will it travel? Firstly, change the 3 minutes into 180 seconds, so that the units are consistent. Now rearrange the first equation to get distance = speed × time. Therefore distance travelled = 10 × 180 = 1800m = 1.8km

Velocity and Acceleration

Velocity is the speed of a particle and its direction of motion (therefore velocity is a vector quantity, whereas speed is a scalar quantity).

When the velocity (speed) of a moving object is increasing we say that the object is accelerating . If the velocity decreases it is said to be decelerating. Acceleration is therefore the rate of change of velocity (change in velocity / time) and is measured in m/s².

A car starts from rest and within 10 seconds is travelling at 10m/s. What is its acceleration?

Distance-Time Graphs

These have the distance from a certain point on the vertical axis and the time on the horizontal axis. The velocity can be calculated by finding the gradient of the graph. If the graph is curved, this can be done by drawing a chord and finding its gradient (this will give average velocity) or by finding the gradient of a tangent to the graph (this will give the velocity at the instant where the tangent is drawn).

Velocity-Time Graphs/ Speed-Time Graphs

A velocity-time graph has the velocity or speed of an object on the vertical axis and time on the horizontal axis. The distance travelled can be calculated by finding the area under a velocity-time graph. If the graph is curved, there are a number of ways of estimating the area (see trapezium rule below). Acceleration is the gradient of a velocity-time graph and on curves can be calculated using chords or tangents, as above.

The distance travelled is the area under the graph. The acceleration and deceleration can be found by finding the gradient of the lines.

On travel graphs, time always goes on the horizontal axis (because it is the independent variable).

Trapezium Rule

This is a useful method of estimating the area under a graph. You often need to find the area under a velocity-time graph since this is the distance travelled.

Area under a curved graph = ½ × d × (first + last + 2(sum of rest))

d is the distance between the values from where you will take your readings. In the above example, d = 1. Every 1 unit on the horizontal axis, we draw a line to the graph and across to the y axis. 'first' refers to the first value on the vertical axis, which is about 4 here. 'last' refers to the last value, which is about 5 (green line).] 'sum of rest' refers to the sum of the values on the vertical axis  where the yellow lines meet it. Therefore area is roughly: ½ × 1 × (4 + 5 + 2(8 + 8.8 + 10.1 + 10.8 + 11.9 + 12 + 12.7 + 12.9 + 13 + 13.2 + 13.4)) = ½ × (9 + 2(126.8)) = ½ × 262.6 = 131.3 units²

TOM ROCKS MATHS

Maths, but not as you know it…, gcse maths: travel graphs (speed-distance-time).

Learn how to use travel graphs relating speed, distance and time to solve problems. Tom introduces the topic, Bobby applies it to Usain Bolt’s 100-metre world record, and Susan uses an interactive tool on GeoGebra – go to www.geogebra.org/m/ABuBYdX7 to join in at home. 

This is the second lesson in a new series with the Maths Appeal duo – Bobby Seagull and Susan Okereke – and Tom Rocks Maths where we’ll be exploring the GCSE Maths syllabus to show the world that maths is accessible to everyone!

Watch Bobby and Susan answer YOUR questions here .

Watch Tom’s livestream here .

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)
• Click to share on Reddit (Opens in new window)
• Click to share on LinkedIn (Opens in new window)
• Click to email a link to a friend (Opens in new window)
• Click to share on Pinterest (Opens in new window)
• Click to share on WhatsApp (Opens in new window)
• Click to share on Tumblr (Opens in new window)

[…] Watch the video for lesson 2 (Travel graphs) here. […]

[…] Watch the video lesson here. […]

Leave a comment Cancel reply

• Already have a WordPress.com account? Log in now.
• Subscribe Subscribed
• Copy shortlink
• Report this content
• View post in Reader
• Manage subscriptions
• Collapse this bar

Real Life Graphs

Four lessons in this section:

Conversion graphs is a complete lesson with a discussion starter and three visual explanations. Includes a differentiated main task and problem-solving questions.

Real life graphs features distance-time graphs and capacity-time graphs. Pair-work and differentiated main task, with literacy story-telling plenary.

Using gradients of line segments to calculate speed from distance-time graphs.

Area under graphs is a complete lesson on area under graphs and gradient, velocity-time graphs and acceleration/deceleration. Clear explanation, Bloom's Taxonomy questions and a differentiated main task.

Visual maths worksheets, each maths worksheet is differentiated and visual.

Travel Graphs GCSE Questions PDF

Total reviews: (0), travel graphs gcse revision description.

This set of questions provides travel graphs in the form of distance-time graphs. Learners will need to read information from the graphs, such as distances at certain times and periods of rest. They will also need to calculate the speed between different times.

WE LOVE TO GET YOUR FEEDBACK:

📝 NEW NATIONAL NUMERACY DAY WORKSHEETS ADDED - CLICK HERE TO DOWNLOAD NOW ✅

Thank you for submitting the form

Get 20 FREE MATHS WORKSHEETS

Fill out the form below to get 20 FREE maths worksheets!

To use this resource a subscription to Go Teach Maths is required. A subscription gives you access to every resource on the website!

Individual Subscription

School subscription.

• Comprehensive topic coverage
• Over 7000 classroom resources
• GCSE & IGCSE coverage

A subscription to Go Teach Maths gives you access to every resource on the website!

Log in to your individual or school account

Or subscribe from only £25 per year!

Reset your password

Please enter the registered email address for your individual or school subscription.

Distance-Time Graphs: Constant Speeds

Presentations.

Demonstration

Card Complete & Match

Teacher-Led Activities

Teacher-Led Activity

Exam Questions

AQA Foundation

9-1 Foundation

2-Minute Feedback Form

[email protected]

• About Go Teach Maths
• What Do Teachers Say About GTM?
• Terms & Conditions

© Go Teach Maths

Privacy Overview

Real Life Graphs: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

Mathster keyboard_arrow_up Back to Top

Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

Corbett Maths keyboard_arrow_up Back to Top

Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.

• International
• Schools directory
• Resources Jobs Schools directory News Search

Travel Graphs -EdExcel 1MA1 Questions

Subject: Mathematics

Age range: 14-16

Resource type: Assessment and revision

Last updated

26 August 2020

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

The Ultimate Collection of ALL questions on DISTANCE/TIME & SPEED/TIME GRAPHS from EdExcel 1MA1 9-1 GCSE Mathematics - FREE . All questions from past papers, specimen papers, sample papers are included. Clues and fully worked model solutions/answers available free from mathsupgrade.co.uk .

• Complete coverage of the topic
• Separated into non-calculator and calculator sections, each section graduated from easiest to hardest - suitable for both Foundation and Higher
• Number of marks in brackets after each question
• Suitable for use as in-class worksheet, as an assessment, or set as revision homework
• Designed for EdExcel, but also useful for AQA, OCR & WJEC
• Eco friendly - unnecessary white space removed
• Regularly updated with new questions
• All completely free
• High quality exam booklets, clues and fully worked model solutions available for EVERY topic free from mathsupgrade.co.uk .

Creative Commons "NoDerivatives"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

Great resource. Thank you for sharing.

mathsupgrade_co_uk

Thanks for the kind review kooldude! Please visit mathsupgrade.co.uk for question booklets and worked model solutions on every topic for EdExcel 1MA1.

Empty reply does not make any sense for the end user

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: