Calculating displacement using a velocity-time graph - Higher
The area under the graph can be calculated by:
- using geometry (if the lines of the graph are straight)
- counting the squares beneath the line (particularly if the lines of the graph are curved)
Example
Calculate the total displacement of the object, whose motion is represented by the velocity-time graph below.
The displacement can be found by calculating the total area of the shaded sections between the line and the time axis.
There is a triangle and a rectangle 鈥 the area of both must be calculated and added together to give the total displacement.
To find the area of the triangle:
area = \(\frac{\text{1}}{\text{2}}\) x base x height
area = \(\frac{\text{1}}{\text{2}}\) x 4 s x 8 m/s = 16m
To find the area of the rectangle:
area = base 脳 height
area = (10 - 4) s 脳 8 m/s = 48 m
Add the areas together to find the total displacement:
Total displacement = (16 m + 48 m) = 64 m
| Velocity-time graph | Speed-time graph | |
| Gradient of graph | Acceleration (m/s2) | Rate of Change of Speed (m/s2) |
| Area under graph | Displacement (m) | Distance (m) |
| Gradient of graph | |
| Velocity-time graph | Acceleration (m/s2) |
| Speed-time graph | Rate of Change of Speed (m/s2) |
| Area under graph | |
| Velocity-time graph | Displacement (m) |
| Speed-time graph | Distance (m) |