Mechanics: Displacement-Time Graphs

Definition of Displacement-Time Graphs

Displacement-time Graphs are a graphical representation of the object’s movement.
The x-axis represents the time that has elapsed, and the y-axis represents the displacement from the starting position.

A straight line on a displacement-time graph shows uniform motion. This means that the object is moving at a constant speed.
A horizontal line represents an object at rest as there is no change in displacement over time.
An inclined straight line indicates movement at a constant speed with positive slope showing motion in a positive direction and a negative slope showing motion in a negative direction.
The slope of the graph indicates the velocity of the object. A steep slope represents a higher velocity and a shallow slope represents a lower velocity.
A curved line on a displacement-time graph indicates non-uniform motion or acceleration. This means that the object is either speeding up or slowing down.

Calculate the velocity by finding the slope of the graph. The formula is v = ∆d / ∆t, where ∆d is change in displacement and ∆t is time taken.
A displacement-time graph does not directly show the acceleration of an object. However, if the graph is curved, it indicates accelerated motion.
For curved lines, the velocity can be determined for any point by calculating the slope of the line that is tangent to that point.

It is crucial to understand the units used in the graph: Time is generally given in seconds (s), and Displacement is usually given in metres (m).
When analysing displacement-time graphs, always label the axes correctly with corresponding quantities and units.