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{{T}}
[[Category:English]]
[[Category:Distance-Time Graphs]]

{{BR}}
= Introduction =

A '''distance-time graph''' shows how the total distance travelled by an object changes as time passes. It turns a journey into a picture that you can read, compare, and calculate from. In Grades 7–8, distance-time graphs connect ideas from [[English:Mathematics|Mathematics]], [[English:Physics|Physics]], and everyday motion.

On a standard distance-time graph, '''time''' is placed on the horizontal x-axis and '''distance''' is placed on the vertical y-axis. Each point tells you how much distance has been travelled by a particular time. The slope, also called the [[English:Slope|gradient]], tells you about speed: a steeper line means more distance is covered in the same amount of time.

[[File:Distance-time graph example.svg|500px|frameless|center]]

The graph above is a verified Wikimedia Commons example of a distance-time graph. As you work through this aiMOOC, focus on what the shape of each section says about motion.

{{#ev:youtube|https://www.youtube.com/watch?v=lrHAnr9cYdQ|500|center}}

This FuseSchool video gives a visual introduction to reading distance-time graphs.

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= Learning Goals =

By the end of this aiMOOC, you should be able to read axes and units correctly, describe motion from the shape of a graph, calculate average speed from a straight section, compare the speeds of two objects, plot a distance-time graph from a data table, explain what a horizontal section means, and distinguish a distance-time graph from a position-time graph.

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= Understanding Distance-Time Graphs =

{{BR}}
== Axes, Units, and Points ==

A graph is only meaningful when its axes are labelled clearly. The x-axis normally shows time in seconds, minutes, or hours. The y-axis normally shows distance in metres or kilometres. The units must be read before you calculate anything.

For example, the point at 3 minutes and 180 metres means that by 3 minutes, the object has travelled 180 metres. A point does not by itself tell you whether the object was moving quickly or slowly just before that time. To study speed, you compare two points and examine the slope between them.

{| class="wikitable"
! Graph feature
! What to check
! Example
|-
| Horizontal axis
| Time and its unit
| Time in seconds
|-
| Vertical axis
| Distance and its unit
| Distance in metres
|-
| A plotted point
| Distance reached at a given time
| 120 metres after 30 seconds
|-
| A line segment
| How distance changes during a time interval
| Constant, zero, or changing speed
|}

{{BR}}
== Straight Lines and Constant Speed ==

A straight rising line has a constant slope. On a distance-time graph, this means the object is travelling at a '''constant speed'''. Equal increases in time produce equal increases in distance.

[[File:UniformMotion.gif|500px|frameless|center]]

The animation illustrates uniform motion. When motion is uniform, the distance increases steadily with time.

[[File:Uniform motion graph 03.jpg|500px|frameless|center]]

A steeper straight line represents a greater constant speed because the object covers more distance during the same time interval.

{{BR}}
== Horizontal Lines and Rest ==

A horizontal line means that time is passing but the distance is not increasing. The object is therefore '''stationary''' during that interval.

Imagine that a cyclist reaches 600 metres after 4 minutes and is still at 600 metres after 6 minutes. The graph is horizontal from 4 to 6 minutes. The cyclist has stopped for 2 minutes.

A horizontal line does '''not''' mean time has stopped. It means the measured distance stays unchanged while time continues.

{{BR}}
== Calculating Speed from the Slope ==

For a straight section of a distance-time graph, calculate speed with:

'''speed = change in distance ÷ change in time'''

If an object travels from 40 metres at 10 seconds to 160 metres at 30 seconds, the change in distance is 120 metres and the change in time is 20 seconds.

'''speed = 120 m ÷ 20 s = 6 m/s'''

The same idea works with kilometres and hours. If you divide kilometres by hours, your answer is in kilometres per hour.

For a straight line, the slope is constant, so the calculated speed is the same anywhere on that section. For a curved line, the slope changes, so the speed changes.

{{#ev:youtube|https://www.youtube.com/watch?v=RM02SnuJ0MY|500|center}}

This Cognito video reinforces how distance-time graphs show motion and how their gradients relate to speed.

{{BR}}
== Curved Lines and Changing Speed ==

A curved distance-time graph shows that the slope is changing. This means the speed is changing.

If a curve becomes '''steeper''' as time passes, the object is speeding up. If a curve becomes '''less steep''' and starts to flatten, the object is slowing down. At this level, you can often describe the change by comparing the steepness of the graph at different times instead of calculating an exact instantaneous speed.

[[File:1-D kinematics.svg|500px|frameless|center]]

This kinematics diagram links position, velocity, and acceleration as functions of time. It goes beyond the basic course, but it helps you see how different motion graphs describe the same movement in different ways.

{{BR}}
== Distance and Position Are Not the Same ==

'''Distance''' is the total length of the path travelled. It cannot decrease as a journey continues. If you walk 100 metres away from your starting point and then walk 40 metres back, your total distance travelled is 140 metres.

'''Position''' describes where you are relative to a chosen reference point, while [[English:Displacement|displacement]] is the change in position. Position can increase or decrease. Because of this, a position-time graph may slope downward when an object moves back toward the reference point.

[[File:Distancedisplacement.png|500px|frameless|center]]

This distinction prevents a common mistake. On a true distance-time graph of total distance travelled, a downward-sloping section would not make physical sense because total distance cannot be undone.

{{BR}}
= Worked Example: A Walk with a Stop =

A student walks along a path. The recorded data are:

{| class="wikitable"
! Time in minutes
! Distance in metres
|-
| 0
| 0
|-
| 2
| 120
|-
| 4
| 240
|-
| 6
| 240
|-
| 8
| 400
|}

From 0 to 4 minutes, the student travels 240 metres in 4 minutes. The speed is '''60 m/min'''.

From 4 to 6 minutes, the distance stays at 240 metres. The speed is '''0 m/min''', so the student is stopped.

From 6 to 8 minutes, the student travels another 160 metres in 2 minutes. The speed is '''80 m/min'''.

The last moving section is steeper than the first moving section, so the student moves faster after the stop.

{{#ev:youtube|https://www.youtube.com/watch?v=HYPWbcyMq2c|500|center}}

Use this additional explanation to review how speed can be found from a distance-time graph.

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= Plotting Your Own Graph =

Start with a data table that records time and total distance. Put time on the x-axis and distance on the y-axis. Choose a sensible scale that uses most of the graph area. Label both axes and include units. Plot each point accurately. Join the points in the way that best represents the data, then give the graph a clear title.

Before interpreting the graph, check that your scales increase evenly. A scale such as 0, 10, 20, 30 is evenly spaced. A scale such as 0, 10, 50, 60 at equal gaps would be misleading.

{{BR}}
== Reading a Multi-Stage Journey ==

Many real journeys contain several stages. A graph might show a person walking, stopping, and then walking faster. Read one section at a time.

A useful method is to ask four questions for every section: Does the distance increase? Is the line horizontal? How steep is the line? Does the steepness stay constant or change?

When two straight sections both rise, the steeper section represents the higher speed. When two objects are shown on the same axes, you can compare their slopes directly only if the axes and scales are the same.

{{BR}}
= Common Mistakes =

'''Mixing up the axes:''' time usually belongs on the x-axis and distance on the y-axis.

'''Ignoring units:''' 300 metres in 60 seconds is not the same speed as 300 kilometres in 60 hours.

'''Using total distance instead of change in distance for one section:''' when you calculate the speed of a section that does not begin at the origin, subtract the starting distance from the ending distance.

'''Thinking a horizontal line means constant non-zero speed:''' on a distance-time graph, a horizontal line means zero speed.

'''Thinking a steeper line means more time:''' steepness compares distance change with time change. A steeper line means greater speed.

'''Allowing total distance to decrease:''' a true distance-time graph of cumulative distance should stay level or rise, not fall.

{{BR}}
= Why Distance-Time Graphs Matter =

Distance-time graphs help you turn recorded measurements into evidence about motion. They are useful in school experiments, sport, transport, journey planning, robotics, and any investigation where you need to compare how far something travels over time.

The skill also prepares you for later work with [[English:Speed|Speed]], [[English:Velocity|Velocity]], [[English:Acceleration|Acceleration]], [[English:Functions|Functions]], and other kinds of motion graphs.

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= Interactive Tasks =

{{BR}}
== Quiz: Test Your Knowledge ==

{{MC}}

'''Which quantity is normally shown on the horizontal axis of a distance-time graph?'''
(Time)
(!Distance)
(!Speed)
(!Mass)

{{E}}
<br>

{{MC}}

'''What does a horizontal section of a distance-time graph show?'''
(The object is stopped)
(!The object is speeding up)
(!The object is moving at constant nonzero speed)
(!The clock has stopped)

{{E}}
<br>

{{MC}}

'''Which formula gives average speed?'''
(Distance divided by time)
(!Time divided by distance)
(!Distance multiplied by time)
(!Distance added to time)

{{E}}
<br>

{{MC}}

'''An object travels 150 metres in 30 seconds. What is its average speed?'''
(5 metres per second)
(!30 metres per second)
(!120 metres per second)
(!4500 metres per second)

{{E}}
<br>

{{MC}}

'''What does a steeper straight line mean on the same distance-time axes?'''
(A greater constant speed)
(!A smaller constant speed)
(!A longer stop)
(!A smaller distance)

{{E}}
<br>

{{MC}}

'''A graph stays at 400 metres from minute 4 to minute 7. What happened?'''
(The object stopped for three minutes)
(!The object travelled 400 metres in three minutes)
(!The object moved backward)
(!The object doubled its speed)

{{E}}
<br>

{{MC}}

'''What does a curve that becomes steeper usually show?'''
(The object is speeding up)
(!The object is standing still)
(!The object has zero distance)
(!The time scale is decreasing)

{{E}}
<br>

{{MC}}

'''Which quantity is normally shown on the vertical axis of a distance-time graph?'''
(Distance)
(!Time)
(!Temperature)
(!Mass)

{{E}}
<br>

{{MC}}

'''Which statement is true for a graph of total distance travelled?'''
(The graph should not slope downward)
(!The graph must always be horizontal)
(!The graph must always be curved)
(!The graph must end at zero)

{{E}}
<br>

{{MC}}

'''How do you find the average speed for a complete journey?'''
(Divide total distance by total time)
(!Divide final distance by starting distance)
(!Multiply total time by total distance)
(!Subtract total time from total distance)

{{E}}
<br>

{{BR}}
== Memory Game ==

<div class="memo-quiz">
{|
|-
| Distance || Total length of the path travelled
|-
| Time || How long the motion lasts
|-
| Gradient || Steepness that represents speed
|-
| Stationary || Not changing distance while time passes
|-
| ConstantSpeed || Equal distances covered in equal time intervals
|-
| AverageSpeed || Total distance divided by total time
|}
{{E}}
<br>

{{BR}}
== Drag and Drop ==

<div class="lueckentext-quiz">

{| class="wikitable"
! Match the correct terms.
! Topic
|-
| '''Time axis'''
| Horizontal axis
|-
| '''Distance axis'''
| Vertical axis
|-
| '''Horizontal segment'''
| Object is stopped
|-
| '''Steeper segment'''
| Greater speed
|-
| '''Curved segment'''
| Changing speed
|}
{{E}}

<br>
...
<br />

{{BR}}
== Crossword Puzzle ==

<div class="kreuzwort-quiz">
{|
|-
| Distance || What total path length is shown on the vertical axis?
|-
| Gradient || What word means the steepness of a graph?
|-
| Stationary || What describes an object whose distance is not changing?
|-
| Constant || What kind of speed is shown by a straight rising line?
|-
| Average || What kind of speed uses total distance divided by total time?
|-
| Interval || What word means a selected period between two times?
|}
{{E}}
<br>

{{BR}}
== LearningApps ==

<iframe> https://learningapps.org/index.php?s=Distance+Time+Graphs </iframe>

{{BR}}
== Cloze Text ==

<quiz display=simple>
{'''Complete the text.'''<br>
|type="{}"}
A distance-time graph usually places { time } on the horizontal axis. The vertical axis shows { distance }. The slope of a straight rising line represents { speed }. A horizontal line shows that the object is { stationary }. A steeper straight section represents a { faster } speed. You calculate average speed by dividing total distance by total { time }. A curve that becomes steeper shows that the speed is { increasing }. A true graph of total distance travelled should not slope { downward }.
</quiz>

<br>

{{BR}}
= Open-Ended Tasks =

{{BR}}
=== Easy ===
# [[English:Walk and Record|Walk and Record]]: Walk a measured route, record your distance every 10 seconds, and plot the results on a distance-time graph.
# [[English:Journey Story|Journey Story]]: Write a short story that includes moving, stopping, and moving faster, then sketch the distance-time graph that matches it.
# [[English:Graph Hunt|Graph Hunt]]: Find three graphs in textbooks, posters, or trusted websites and explain which features help you recognize a distance-time graph.
# [[English:Draw a Journey|Draw a Journey]]: Create a neat distance-time graph for a person who walks at constant speed, stops, and then continues at a faster speed.

{{BR}}
=== Standard ===
# [[English:Toy Car Investigation|Toy Car Investigation]]: Use a toy car, measuring tape, and stopwatch to collect motion data, then calculate average speed for at least two intervals.
# [[English:Compare Two Walkers|Compare Two Walkers]]: Collect or invent realistic data for two walkers on the same route and decide who is faster during each stage using graph slopes.
# [[English:School Journey Model|School Journey Model]]: Model part of a journey to school with a distance-time graph and explain each section in complete sentences.
# [[English:Video Explanation|Video Explanation]]: Record a short teaching video in which you explain axes, slope, horizontal sections, and one speed calculation from a graph.

{{BR}}
=== Advanced ===
# [[English:Data Reliability Study|Data Reliability Study]]: Repeat the same walking experiment three times, compare the graphs, identify measurement uncertainty, and suggest ways to improve the method.
# [[English:Multi-Stage Journey Design|Multi-Stage Journey Design]]: Design a data table and graph for a journey with at least five stages, including two different constant speeds and two stops, then justify every segment.
# [[English:Position versus Distance|Position versus Distance]]: Create one distance-time graph and one position-time graph for a person who walks away from a starting point and then returns, and explain why only one graph can slope downward.
# [[English:Real-World Motion Report|Real-World Motion Report]]: Investigate a real motion example from sport, transport, or robotics, gather suitable data, create a graph, and write a report connecting the slope to speed.

{{:Open Task - Create a MOOC}}

{{BR}}
= Learning Assessment =

# [[English:Graph Interpretation Assessment|Graph Interpretation Assessment]]: Explain a multi-stage distance-time graph by identifying periods of rest, constant speed, and changing speed, and support each claim with evidence from the graph.
# [[English:Slope Calculation Assessment|Slope Calculation Assessment]]: Calculate the speed for several straight sections that begin at different times and distances, showing the changes in both distance and time.
# [[English:Graph Construction Assessment|Graph Construction Assessment]]: Convert a data table into a correctly scaled and labelled distance-time graph, then explain why your chosen scale is appropriate.
# [[English:Comparison Assessment|Comparison Assessment]]: Compare two journeys shown on the same axes and decide which object is faster in selected intervals using slope rather than visual guesswork.
# [[English:Error Analysis Assessment|Error Analysis Assessment]]: Examine an incorrect distance-time graph, identify at least three errors, and explain how each error changes or confuses the meaning.
# [[English:Transfer Assessment|Transfer Assessment]]: Design a distance-time graph for a new real-life situation and explain how someone could use it to make a prediction about motion.

<br>
<br>

{{BR}}
= Evidence of Learning =

Strong evidence of learning includes both what you understand and what you can do.

{| class="wikitable"
! Evidence type
! What successful learning looks like
|-
| Knowledge
| You can explain axes, units, slope, constant speed, changing speed, rest, and the difference between distance and position.
|-
| Skills
| You can read coordinates, calculate changes, find average speed, compare slopes, select scales, and plot accurate points.
|-
| Products
| You can produce a labelled graph, a data table, a written motion story, and a short explanation supported by calculations.
|-
| Investigation
| You can collect distance and time data safely, repeat measurements, notice uncertainty, and improve your method.
|-
| Transfer
| You can apply graph-reading skills to unfamiliar journeys, experiments, sports data, transport situations, and later work on velocity and acceleration.
|}

<br>
<br>

{{BR}}
= OERs on the Topic =

The English Wikipedia article on [[English:Speed|Speed]] provides useful background on average speed, instantaneous speed, and the relationship between speed and the slope of a distance-time graph.

<iframe> https://en.m.wikipedia.org/wiki/Speed </iframe>

<br>

{{BR}}
= Linked Learning Areas =

Distance-time graphs connect measurement, proportional reasoning, geometry, data interpretation, and motion. The most important linked ideas are gathered below.

{| align=center
{{:D-Tab}}
'''[[English:Distance-Time Graphs|Distance-Time Graphs]]'''
# [[English:Distance|Distance]]
# [[English:Time|Time]]
# [[English:Speed|Speed]]
# [[English:Slope|Slope]]
# [[English:Motion|Motion]]
# [[English:Kinematics|Kinematics]]
# [[English:Functions|Functions]]
|}

[[Category:English]]
[[Category:Grades 7-8]]

{{BR}}
= aiMOOC Projects =
[[Category:English]]
[[Category:Distance-Time Graphs]]
[[Category:Mathematics]]
[[Category:Physics]]
[[Category:Science]]
[[Category:Graphs]]
[[Category:Kinematics]]
[[Category:Grades 7-8]]
[[Category:AI_MOOC]]
[[Category:GPT aiMOOC]]
{{MT}}

English:Distance-Time Graphs - Versionsgeschichte

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