Graphs of Motion
How Graphs Tell Motion Stories
Position-time graphs
A position-time graph shows how position changes with time. The slope of this graph gives velocity. A steeper slope means a larger velocity.
Velocity-time graphs
A velocity-time graph shows how velocity changes with time. The slope gives acceleration, and the area under the graph gives displacement.
Acceleration-time graphs
An acceleration-time graph tells how acceleration changes with time. The area under the graph gives the change in velocity, .
Graph connections
Slope means "rate of change." Area means "accumulated change." These two ideas appear again and again in physics.
Graph interpretations
| Graph | Slope means | Area means |
|---|---|---|
| Position-time | Velocity | Not usually used directly |
| Velocity-time | Acceleration | Displacement |
| Acceleration-time | Jerk-related change | Change in velocity |
What does the slope of a velocity-time graph represent?
Slope on a velocity-time graph is acceleration.
Correct answer: Acceleration
What does the area under a velocity-time graph represent?
The area gives the change in position.
Correct answer: Displacement
How to read a motion graph
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1
Step 1: Identify the axes and units.
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2
Step 2: Decide whether slope or area is useful.
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Step 3: Relate graph features to motion words like faster, slower, or changing direction.
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Step 4: Check whether the graph shows velocity, position, or acceleration.