Interpreting Enclosed Areas in Velocity-Time Graphs to Determine Distance Travelled or Displacement

Velocity-time graphs tell us a lot about how an object moves — including its acceleration and changes in velocity. One of the most important things you can calculate from these graphs is the distance travelled or displacement. You do this by interpreting the area between the graph line and the time axis.

How Area Relates to Distance or Displacement

In a velocity-time graph, the area under the line (between the velocity curve and the time axis) represents how far the object travels during a specific time period.

• If the object moves in one direction, the area gives the total distance.

• If the object changes direction (i.e., if velocity goes below the time axis), the area gives the displacement—the overall change in position.

How to Calculate the Area

Follow these steps to find the distance travelled or displacement:

1. Identify the Area of Interest
Find the section of the graph that covers the time interval you're interested in. This is the area between the graph line and the time axis.

2. Break it Into Simple Shapes
Split the area into basic geometric shapes—such as rectangles and triangles—that are easier to calculate.

3. Calculate Each Area
Use appropriate formulas for each shape (e.g. for a triangle, use ½ × base × height).

4. Add or Subtract Areas

• Add all areas if the velocity is positive (above the time axis).

• Subtract any areas below the time axis if calculating displacement.

Example Calculation

Imagine a velocity-time graph where the area under the line forms a triangle.

• Base (time): 5 seconds

• Height (velocity): 15 m/s

Area of triangle = ½ × base × height
= ½ × 5 × 15
= 37.5 m

So, the object travelled 37.5 metres during that time.

Summary

Understanding how to interpret the area under a velocity-time graph is key in physics. By identifying the right section of the graph, breaking it into shapes, and calculating the total area, you can work out how far an object moves — either as distance (total ground covered) or displacement (net change in position). It’s a simple and visual way to understand motion using geometry.