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 & the rate of change of the gradient on 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.