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Position–time graphs
Beginner
The slope of x–t gives velocity.
On an x–t graph, the slope at any point is the velocity. A straight line means constant velocity, a curve means acceleration, and a flat line means rest. Steeper means faster.
A line rising from (0, 0) to (4 s, 20 m) has slope 5 m/s.
A hill-shaped x–t graph is not the path of the object; it's position against time.
In more detail
A position-time graph shows where an object is at each time. Its slope gives the velocity, and a curve means the velocity is changing.
Real-world uses
- Athletics coaches plot a sprinter's position against time to compare acceleration phases.
- Traffic engineers use position-time graphs to study queues and vehicle spacing.
- A physics teacher uses a position-time graph of a trolley to show that a straight line means steady speed and a curve means changing speed.
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Frequently asked questions
What does a horizontal line on a position-time graph mean?
The object is at rest.
What does a steeper slope mean?
A greater velocity in the same direction.
What does a horizontal line on a position-time graph mean?
The object is at rest, because its position does not change with time.
Related topics in Kinematics
Instantaneous velocity · Acceleration · Uniform motion · Velocity–time graphs · Equations of motion: v = u + at · Equations of motion: s = ut + ½at²