# 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.