Velocity-Time Graphs (OCR A Level Maths: Mechanics)

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 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

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

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

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