Motion Graphs

Motion Graphs

Middle School

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Learning Objectives

• Interpret distance-time graphs to describe an object's motion.

• Interpret speed-time graphs to describe an object's motion.

• Differentiate between the graphical representations of motion on distance-time and speed-time graphs.

• Analyze the slope of a line on a motion graph to determine speed and acceleration.

Key Vocabulary

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Distance-Time Graph

This graph shows how an object's distance from a point changes over a period of time.

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Speed-Time Graph

This graph shows how an object's speed changes over a specific period of time.

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Slope

Slope is the steepness of a line on a graph, representing speed on a distance-time graph.

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Constant Speed

Movement where the speed does not change, shown as a straight line on a distance-time graph.

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Acceleration

Acceleration is the rate of change of velocity, shown by a curved line on a distance-time graph.

Interpreting Distance-Time Graphs

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Constant Speed

• A straight diagonal line shows an object moving at a constant speed.

• The steepness of the line shows how fast the object is moving.

• A steeper line means a faster speed compared to a shallower line.

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No Motion

• A flat, horizontal line means the object is not moving at all.

• This shows that the object's distance from the start is not changing.

• The object is stopped, so its speed during this time is zero.

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Returning to Start

• A downward-sloping line shows the object moving back toward its starting point.

• This means the object's distance from the starting point is getting smaller.

• The object has returned to the start when the line touches the x-axis.

Multiple Choice

On a distance-time graph, what does a flat, horizontal line signify?

• The object is moving at a constant speed.

• The object is stopped or not moving.

• The object is accelerating.

• The object is returning to the starting point.

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Acceleration on Distance-Time Graphs

Increasing Speed

• A curved line on a distance-time graph shows that an object's speed is changing, which is acceleration.

• An upward-curving line that gets steeper shows that the object is speeding up, covering more distance over time.

Decreasing Speed

• A line that curves to become flatter and less steep shows that the object is slowing down.

• This change in speed, or slowing down, is also a type of acceleration known as deceleration.

Multiple Choice

How is increasing speed (acceleration) represented on a distance-time graph?

• A straight diagonal line.

• A flat horizontal line.

• An upward-curving line.

• A downward-sloping line.

Interpreting Speed-Time Graphs

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Constant Speed

• A flat, horizontal line shows the object's speed is constant.

• The line is above the zero mark on the speed axis.

• The object is moving but its speed is not changing.

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Acceleration

• An upward-sloping line shows the object is accelerating or speeding up.

• This means the object’s speed is increasing steadily over time.

• The steeper the line, the greater the rate of acceleration.

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Deceleration

• A downward-sloping line shows the object is decelerating or slowing down.

• This means the object’s speed is decreasing steadily over time.

• A line on the zero axis means the object is stopped.

Multiple Choice

On a speed-time graph, what does a straight, upward-sloping diagonal line represent?

• The object is stopped.

• The object is moving at a constant speed.

• The object is accelerating.

• The object is decelerating.

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Distance-Time vs. Speed-Time Graphs

Distance-Time Graphs

• Constant speed is shown as a straight line sloping diagonally upward.

• A flat, horizontal line on the graph means the object is not moving.

• Acceleration is represented by a line that curves upward from left to right.

Speed-Time Graphs

• Constant speed is represented by a flat, horizontal line above the zero mark.

• A flat line along the zero mark indicates that the object is stopped.

• A straight, upward-sloping diagonal line is used to show steady acceleration.

Multiple Choice

How is 'no motion' represented differently on a Distance-Time graph compared to a Speed-Time graph?

• It's a curved line on both.

• It's a flat horizontal line on a D-T graph and a flat line at zero on an S-T graph.

• It's a diagonal line on a D-T graph and a curved line on an S-T graph.

• It's a flat line at zero on a D-T graph and a flat horizontal line on an S-T graph.

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Common Misconceptions

Misconception	Correction
A flat line always means an object is stopped.	On a speed-time graph, it means the object is moving at a constant speed.
A straight, diagonal line always shows constant speed.	On a speed-time graph, this line shows constant acceleration (a change in speed).
The line's shape is the only important feature.	Always check the axis labels (y-axis and x-axis) to understand the graph.

Multiple Choice

A speed-time graph shows a flat horizontal line above zero, which then becomes a downward sloping diagonal line to zero. What motion does this represent?

• Accelerating and then stopping.

• Moving at a constant speed and then decelerating to a stop.

• Remaining stopped and then accelerating.

• Decelerating and then moving at a constant speed.

Multiple Choice

Which option best describes a journey on a distance-time graph that starts with acceleration, moves to a constant speed, and then stops?

• A straight diagonal line, a curve, then a flat horizontal line.

• A flat horizontal line, a straight diagonal line, then a curve.

• An upward curve, a straight diagonal line, then a horizontal line.

• A downward curve, a horizontal line, then a straight diagonal line.

Multiple Choice

A distance-time graph for two cyclists shows two straight lines starting from the origin. Line A is steeper than Line B. If both cyclists finish a 10-mile race, what can you conclude?

• Cyclist A finished the race in less time than Cyclist B.

• Cyclist B was faster than Cyclist A.

• Both cyclists finished at the same time.

• Cyclist A stopped during the race.

Multiple Choice

A car starts from rest and accelerates uniformly. If you were to plot this on a speed-time graph and a distance-time graph, what would the lines look like?

• S-T: Flat line; D-T: Straight diagonal line

• S-T: Straight diagonal line from the origin; D-T: Upward-curving line from the origin

• S-T: Upward-curving line; D-T: Straight diagonal line

• S-T: Straight diagonal line from the origin; D-T: Straight diagonal line from the origin

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Summary

• On a distance-time graph, a straight line shows constant speed; a horizontal line is no motion.

• On a speed-time graph, a horizontal line shows constant speed; a diagonal line is acceleration.

• The slope of a distance-time graph tells you the object’s speed.

• Always check the axes of a motion graph to understand what it represents.

Poll

On a scale of 1-4, how confident are you about interpreting motion graphs?

• 1

• 2

• 3

• 4