Motion Graphs (Cambridge International A-Level Physics)

Motion graphs

• There are five types of graph that can represent motion

Distance-time graphs

• On a distance-time graph…

  • slope equals speed
  • the y-intercept equals the initial position
  • a straight(diagonal) line represents a constant speed
  • a curved line represents an acceleration
  • the slope is always zero or positive because distance is a scalar quantity
  • a zero slope (horizontal line) represents a state of rest
  • the area under the curve is meaningless

Displacement-time graphs

• On a displacement-time graph…

  • slope equals velocity
  • the y-intercept equals the initial position
  • a straight(diagonal) line represents a constant velocity
  • a curved line represents an acceleration
  • a positive slope represents motion in the positive direction
  • a negative slope represents motion in the negative direction
  • a zero slope (horizontal line) represents a state of rest
  • the area under the curve is meaningless

Displacement-time graphs for different scenarios

The displacement-time graph for constant velocity is a straight diagonal line, and for acceleration is a curve

Speed-time graphs

• On a speed-time graph…

  • slope equals acceleration
  • the y-intercept equals the initial speed
  • a straight line represents uniform acceleration
  • a curved line represents non-uniform acceleration
  • a positive slope represents an increase in speed
  • a negative slope represents a decrease in **speed **
  • a zero slope (horizontal line) represents motion with constant speed
  • the area under the curve equals the** distance** travelled

Velocity-time graphs

• On a velocity-time graph…

  • slope equals acceleration
  • the y-intercept equals the initial velocity
  • a straight line represents uniform acceleration
  • a curved line represents non-uniform acceleration
  • a positive slope represents an increase in velocity in the positive direction
  • a negative slope represents an increase in velocity in the negative direction
  • a zero slope (horizontal line) represents motion with constant velocity
  • the area under the curve equals the displacement

Velocity-time graphs for different scenarios

The velocity-time graph for constant velocity is a straight horizontal line, for acceleration is a straight diagonal line and for increasing acceleration is a curve

Acceleration-time graphs

• On an acceleration-time graph…

  • slope is meaningless
  • the y-intercept equals the initial acceleration
  • a zero slope (horizontal line) represents an object undergoing constant acceleration
  • the area under the curve equals the change in velocity

Acceleration-time graph for different scenarios

The acceleration-time graph for constant velocity is blank, for increasing velocity is a straight horizontal line and for increasing acceleration is a straight diagonal line

Exam Hint Always check the axes when dealing with graphs. The differences between distance-time graphs and displacement-time graphs, and speed-time graphs and velocity-time graphs are subtle but important. Make sure you know what you are looking at before answering any graph questions in the exam.