Velocity-Time Graphs (Cambridge International A-Level Mathematics)

Velocity-time graphs

What is a velocity-time graph?

• Velocity- time graphs show the velocity of an object as it moves in a straight line
• They show velocity (on the vertical axis) against time (on the horizontal axis)
• Velocity-time graphs can go below the horizontal axis whereas speed-time graphs can not

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

• The gradient of the graph equals the acceleration of an object

• A straight line shows that the object is accelerating at a constant rate

• A horizontal line shows that the object is moving at a constant velocity

• The area between the graph and the x-axis tells us the change in displacement of the object

  • Graph above the x-axis means the object is moving forwards
  • Graph below the x-axis means the object is moving backwards

• The **total displacement **of the object from its starting point is the sum of the areas above the x-axis minus the sum of the areas below the x-axis

• The** total distance travelled **by the object is the sum of all the areas

• If the graph touches the x-axis then the object is** stationary** at that time

• If the graph is above the x-axis then the object has positive velocity and is travelling forwards

• If the graph is below the x-axis then the object has negative velocity and is travelling backwards

Worked Example The motion of a bird travelling in a straight line is tracked for 60 seconds.

This information is displayed in the velocity-time graph below.

(a) Calculate the acceleration of the bird at 20 seconds.

Answer:

(b) Calculate the distance travelled in the first 28 seconds.

Answer:

(c) Calculate the displacement of the bird from its starting point after 60 seconds.

Answer:

Exam Hint

• Be careful to spot if you are working with a distance-time graph or a velocity-time graph.
• Be careful to spot if you are working with a speed-time graph or a velocity-time graph.
• Check where the graph starts from on the y-axis, the velocity does not have to start at 0. For example, the scenario could be a car driving at a constant speed and the driver sees a hazard.
• Be extra vigilant when working with negative gradients or with graphs under the x-axis, it is easy to make mistakes with these.
• Speed is a scalar so it can not be negative whereas velocity can be. Make sure your units are consistent.