Displacement-time graphs - Higher
Displacement-time graphs show how the A distance measured in a specified direction. of a moving object changes with time.
A horizontal line on a displacement-time graph shows that the object is stationary (not moving because the displacement does not change)
A sloping line on a displacement-time graph shows that the object is moving.
In a displacement-time graph, the slope or gradient of the line, is equal to the velocity of the object.
The steeper the line (and the greater the gradient) the faster the object is moving.
Example
| Section of graph | What is represented |
| O - A | Positive constant velocity |
| velocity = gradient of displacement-time graph = displacement ÷ time | |
| displacement = 4 m – 0 m = 4 m | |
| time = 2 s – 0 s = 2 s | |
| velocity = displacement ÷ time = 4 m ÷ 2 s = 2 m/s | |
| A - B | Stopped |
| the displacement does not change: velocity = 0 m/s | |
| B - C | Negative constant velocity |
| the object is now travelling in the opposite direction | |
| velocity = gradient of displacement-time graph = displacement ÷ time | |
| displacement = 0 m – 4 m = -4 m | |
| time = 8 s – 7 s = 1 s | |
| velocity = displacement ÷ time = -4 m ÷ 1 s = -4 m/s | |
| At C | the object has returned to its starting position |
| the displacement is once again zero |
| Section of graph | O - A |
|---|---|
| What is represented | Positive constant velocity |
| Section of graph | |
|---|---|
| What is represented | velocity = gradient of displacement-time graph = displacement ÷ time |
| Section of graph | |
|---|---|
| What is represented | displacement = 4 m – 0 m = 4 m |
| Section of graph | |
|---|---|
| What is represented | time = 2 s – 0 s = 2 s |
| Section of graph | |
|---|---|
| What is represented | velocity = displacement ÷ time = 4 m ÷ 2 s = 2 m/s |
| Section of graph | A - B |
|---|---|
| What is represented | Stopped |
| Section of graph | |
|---|---|
| What is represented | the displacement does not change: velocity = 0 m/s |
| Section of graph | B - C |
|---|---|
| What is represented | Negative constant velocity |
| Section of graph | |
|---|---|
| What is represented | the object is now travelling in the opposite direction |
| Section of graph | |
|---|---|
| What is represented | velocity = gradient of displacement-time graph = displacement ÷ time |
| Section of graph | |
|---|---|
| What is represented | displacement = 0 m – 4 m = -4 m |
| Section of graph | |
|---|---|
| What is represented | time = 8 s – 7 s = 1 s |
| Section of graph | |
|---|---|
| What is represented | velocity = displacement ÷ time = -4 m ÷ 1 s = -4 m/s |
| Section of graph | At C |
|---|---|
| What is represented | the object has returned to its starting position |
| Section of graph | |
|---|---|
| What is represented | the displacement is once again zero |