Displacement-Time Graphs

What is a displacement-time graph?

• Displacement-time graphs show the displacement of an object from a fixed origin as it moves in a straight line
• They show displacement (on the vertical axis) against time (on the horizontal axis)
• Displacement-time graphs can go below the horizontal axis whereas distance-time graphs can not
• Distance can not be negative whereas displacement can be

What are the key features of a displacement-time graph?

• The gradient of the graph equals the velocity of the object

• A positive gradient means the object is travelling forwards
• A negative gradient means that the object is travelling backwards
• The steeper the line, the greater the speed
• A straight line shows that the object is moving at a constant velocity
• A curved line shows that the object is accelerating or decelerating
• A horizontal line shows that the object is stationary
• If the graph touches the x-axis, then the object is at the origin at that time

How do I find the average speed and the average velocity of a journey?

• The average speed can not be negative as speed is a scalar quantity and can only take a positive value

• The average velocity is a vector quantity and can be positive, zero or negative

• Be careful to spot if you are working with a displacement-time graph or a velocity-time graph.
• Be careful to spot if you are working with a displacement-time graph or a distance-time graph
• Check where the graph starts from on the y-axis, the object does not have to start at 0. For example, if the graph starts at 100, the scenario could be a student on a walk starting 100 m from their house.
• Distance is a scalar so it can not be negative whereas displacement from a starting point can be.
• Think about the units when calculating, make sure they are consistent.