Distance-Time Graphs

Distance-Time Graphs

Middle School

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Learning Objectives

• Understand what different line shapes mean on a distance-time graph.

• Compare speeds of objects by looking at the steepness of the lines.

• Read a distance-time graph to find distance, time, and rest periods.

• Describe an object’s motion by analyzing the segments of its graph.

Key Vocabulary

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Distance-Time Graph

A graph showing how far an object has moved over a specific period of time.

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Constant Speed

This is when an object covers the same distance in each equal time period.

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Stationary

An object that is not moving or is at rest, shown as a horizontal line.

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Gradient

The steepness of a line on a graph, which indicates the object's speed.

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Acceleration

The rate at which an object's speed increases, shown by an upward-curving line.

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What is a Distance-Time Graph?

• It shows how an object’s distance from a starting point changes over time.

• The y-axis represents distance, and the x-axis represents the time taken.

• A horizontal line means the object is stationary and not moving at all.

• A straight, sloped line shows movement at a constant and steady speed.

Multiple Choice

On a distance-time graph, what does a horizontal line signify about an object's motion?

• The object is moving at a constant speed.

• The object is accelerating.

• The object is stationary or not moving.

• The object is moving backwards.

Interpreting Distance-Time Graphs

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Constant Speed

• ​The steepness, or gradient, of the line indicates the object's speed.

• ​​A steeper line means a greater distance is covered in less time.

• ​This represents a higher speed compared to a less steep line.

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Acceleration

• ​A line that curves upwards indicates the object is speeding up.

• ​​This process of speeding up is also known as acceleration.

• ​The line gets steeper over time, showing the speed is increasing.

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Deceleration

• ​A line becoming less steep shows the object is slowing down.

• ​​This process of slowing down is also known as deceleration.

• ​The line gets flatter over time, showing the speed is decreasing.

Multiple Choice

When comparing two straight lines on the same distance-time graph, what does the steeper line represent?

• A longer distance traveled.

• A higher speed.

• A period of being stationary.

• A slower speed.

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Direction of Movement

Moving Away from Start

• An upward sloping line shows an object moving away from its starting point.

• As time passes, the distance from the starting point gets larger on the graph.

• This represents forward motion, or moving in a positive direction from the origin.

Moving Towards Start

• A downward sloping line shows an object moving back towards its starting point.

• As time passes, the distance from the starting point gets smaller on the graph.

• This represents backward motion, or moving in a negative direction to the origin.

Multiple Choice

If a segment of a distance-time graph slopes downwards, what does this tell us about the object's movement?

• The object is speeding up.

• The object is stationary.

• The object is moving back towards the starting point.

• The object is moving away from the start at a constant speed.

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Common Misconceptions

Misconception	Correction
A horizontal line means constant speed.	A horizontal line means the object is stationary.
A line sloping down means the object is slowing down.	A downward slope means moving back towards the start.
The graph shows the actual path, like a map.	The graph shows distance from a start point over time.

Multiple Choice

A distance-time graph for a car's journey shows a horizontal line for 30 minutes. What does this imply about the car's journey during that time?

• The car was traveling at a constant speed of 30 mph.

• The car traveled 30 miles in that time.

• The car was stopped for 30 minutes.

• The car was accelerating for 30 minutes.

Multiple Choice

A graph shows a student's walk to school. The first segment is a steep, straight line, and the second segment is a less steep, straight line. What can you infer about the student's speed?

• The student walked at a constant speed the whole time.

• The student walked faster during the second segment.

• The student walked faster during the first segment.

• The student stopped walking during the second segment.

Multiple Choice

A cyclist’s journey is plotted on a distance-time graph. The graph shows a straight sloped line upward, followed by a horizontal line, and then another straight sloped line upward with the same steepness as the first. Which option best describes the cyclist’s journey?

• Cycling at a constant speed, stopping for a rest, then cycling back home at the same speed.

• Cycling at a constant speed, stopping for a rest, then continuing away from the start at the same speed.

• Accelerating, moving at a constant speed, then decelerating to a stop.

• Cycling uphill, then on a flat surface, then continuing uphill at the same pace.

Multiple Choice

A person walks away from a bench and then returns to it. On a distance-time graph, how would the return journey be represented?

• A horizontal line

• An upward-sloping line

• A downward-sloping line

• A curved line

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Summary

• A horizontal line on a distance-time graph means the object is stationary.

• A straight, sloped line indicates constant speed; a steeper line means faster speed.

• An upward slope shows movement away, while a downward slope shows movement back.

• A curved line shows that the speed is changing, which means it is accelerating.

Poll

On a scale of 1-4, how confident are you in interpreting distance-time graphs after this review?

• 1

• 2

• 3

• 4