Area under a velocity-time graph
- Velocity-time graphs show the speed and direction of an object in motion over a specific period of time
- The area under a velocity-time graph is equal to the displacement of a moving object
- The area under a graph can be sectioned into triangles and rectangles to make the calculations easier
- The area of a triangle can be found with the following formula:
- The area of a rectangle can be found with the following formula:
- Where:
- = area
- = length of base
- = height
Worked example
The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.
Calculate the displacement of the vehicle at 40 s.
Answer:
Step 1: State how to determine the displacement
- The displacement is equal to the area under a velocity-time graph
Step 2: Determine the scale on the graph
- Each division is
Step 3: Determine the base and height of the graph
- Time = base = 40 s
- Velocity = height = 105 km h–1
Step 4: Convert km h-1 into km s–1
Step 5: Calculate the area under the graph
Area of a right-angled triangle =
Examiner Tip
Always check the values given on the y-axis of a motion graph - students often confuse displacement-time graphs and velocity-time graphs.