Gradient of a Displacement-Time Graph (Cambridge International AS Physics)

Spec point — 2.1.4

Gradient of a displacement-time graph

• Displacement-time graphs show the changing position of an object in motion

• They also show the direction an object is moving with respect to its starting position

  • A positive gradient on a displacement-time graph shows a constant velocity in the positive direction
  • A negative gradient on a displacement-time graph shows a constant velocity in the negative direction

• The gradient (slope) of a displacement-time graph is equal to the velocity

  • The steeper the slope, the greater the velocity

Worked Example A car driver sees a hazard ahead and applies the brakes to bring the car to a stop.

What does the displacement-time graph look like?

Answer:

• When the velocity-time graph is a horizontal line, this means constant velocity

  • This is a straight, diagonal line on a displacement-time graph

• When the velocity-time graph is a diagonal line towards the negative direction, this means decreasing velocity (deceleration)

  • This is a curve with a decreasing gradient on a displacement-time graph

Exam Hint Don’t forget that velocity is a vector quantity; it has a size and a direction. If velocity is initially positive and then becomes negative, then the object has changed direction.