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
- 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
- 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 in the positive direction
- a negative slope represents an increase in speed in the negative direction
- 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
Examiner Tip
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.