Displacement-Time Graphs (OCR AS Maths: Mechanics)

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

(a)   Calculate the velocity of the athlete during the first 2 seconds.

(b)    Describe the motion of the athlete between the times of 2 seconds and 5 seconds.

(c)   Calculate the velocity of the athlete at 10 seconds.

(d)   Find the total distanced travelled by the athlete during the 14 seconds.