High School Physics

# How to determine Acceleration on displacement-time graphs

Last updated on December 26th, 2023 at 09:54 am

In this post, we will see how to determine the acceleration from a displacement-time graph.

• The gradient of a displacement-time graph shows velocity.
• Acceleration is the rate of change of velocity.
• So on a displacement-time graph, acceleration is the rate of change of the gradient.

A graph of displacement against time for an accelerating object always produces a curve.

## Acceleration is the rate of change of the gradient on the displacement-time graph

If the object is accelerating at a uniform rate, then the rate of change of the gradient will be constant.

• Acceleration is shown by a curve with an increasing gradient.
• Deceleration is shown by a curve with a decreasing gradient.

Note the effect of changing the acceleration on the gradient of a displacement-time graph in the following figures.

• When the acceleration is bigger, the displacement-time graph is tighter, because the rate of change of gradient is higher.
• When the acceleration is smaller, the displacement-time graph is less tight, because the rate of change of gradient is lower.
• For deceleration or retardation, the displacement-time graph, the line has a decreasing gradient & curves the other way.

Note that in the case of deceleration, the moving object in question must have been already moving at t = 0. Otherwise, its displacement would be negative.

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