Gradient of a Displacement-Time Graph (Cambridge (CIE) AS Physics) : Revision Note
Gradient of a displacement-time graph
Displacement-time graphs show the changing position of an object in motion
They also show the direction an object is moving with respect to its starting position
A positive gradient on a displacement-time graph shows a constant velocity in the positive direction
A negative gradient on a displacement-time graph shows a constant velocity in the negative direction
The gradient (slope) of a displacement-time graph is equal to the velocity
The steeper the slope, the greater the velocity
Worked Example
A car driver sees a hazard ahead and applies the brakes to bring the car to rest.
What does the displacement-time graph look like?
Answer:
Step 1: Consider the gradient of each part of the graph
When the velocity-time graph is a horizontal line, this means constant velocity
This is a straight, diagonal line on a displacement-time graph
When the velocity-time graph is a diagonal line towards, this means decreasing velocity (deceleration)
This is a curve with a decreasing gradient on a displacement-time graph
Examiner Tips and Tricks
Don’t forget that velocity is a vector quantity; it has a size and a direction. If velocity is initially positive and then becomes negative, then the object has changed direction.
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