How do you read distance on a velocity-time graph?

To find the distance travelled from a velocity-time graph, you calculate the area under the graph.

The area under the curve between two points in time represents the displacement (or distance if the velocity is always positive) covered during that time interval. Different shapes under the graph correspond to different types of motion:

• Constant Velocity: The area is a rectangle.
• Uniform Acceleration: The area is a triangle or a trapezium.
• Varying Velocity: The area might need to be broken down into smaller shapes or calculated using integral calculus (though basic examples often use standard geometric shapes).

Calculating Distance Using Area

As provided in the reference, you can calculate the distance by finding the geometric area of the shape formed between the velocity line and the time axis.

Here are examples based on the shapes commonly found under velocity-time graphs:

Example 1: Uniform Acceleration (Area of a Triangle)

If the velocity increases linearly from 0, the shape under the graph is a triangle.

• Reference Calculation: In the first 10 seconds, if the graph forms a triangle, the distance is calculated as: ½ × base × height = ½ × 10 s × 40 m/s = 200 m.

This calculation shows that for a period of uniform acceleration from rest, the distance is half the product of the time interval and the final velocity.

Example 2: Constant Velocity (Area of a Rectangle)

If the velocity remains constant over a period, the shape under the graph is a rectangle.

• Reference Calculation: From 10 to 20 seconds, if the graph shows a constant velocity, the distance is calculated as: base × height = 10 s × 40 m/s = 400 m.

This calculation demonstrates that for a period of constant velocity, the distance is simply the velocity multiplied by the time interval.

Summary Table

By calculating and summing the areas under the graph for different time intervals, you can determine the total distance travelled.