**Calculating Displacement in a Velocity-Time Graph**

A velocity-time graph is a graphical representation of an object's velocity over a specific period of time. It provides valuable information about the object's motion, including its speed, direction, and changes in velocity. Displacement, on the other hand, refers to the change in position of an object, usually measured in a straight line from the starting point to the ending point.

To calculate the displacement from a velocity-time graph, we need to understand the relationship between velocity and displacement and make use of the graph's characteristics. Here's a step-by-step guide on how to do it:

**Step 1: Understand the Graph**
Firstly, familiarize yourself with the velocity-time graph. The graph typically consists of a horizontal x-axis representing time and a vertical y-axis representing velocity. The slope of the graph at any given point indicates the object's acceleration.

**Step 2: Identify Key Points**
Identify the key points on the graph, such as the starting point, ending point, and any significant changes in velocity. These points will help determine the displacement.

**Step 3: Calculate Area Under the Graph**
To calculate the displacement, we need to find the area under the velocity-time graph. Note that the area above the x-axis represents positive displacement, while the area below the x-axis represents negative displacement.

**Step 4: Divide the Graph into Appropriate Shapes**
Divide the graph into different shapes, such as rectangles, triangles, or trapezoids, to simplify the calculation. The choice of shapes depends on the graph's characteristics.

**Step 5: Calculate the Area of Each Shape**
Calculate the area of each shape by applying the appropriate formula. For rectangles, the area is the product of the length and width. For triangles, the area is half the product of the base and height. For trapezoids, the area is the average of the parallel sides multiplied by the height.

**Step 6: Sum Up the Areas**
Add up the areas of all the shapes to obtain the total area under the graph. Make sure to consider the positive and negative areas separately to account for direction.

**Step 7: Determine Displacement**
Determine the displacement by considering the sign of the total area under the graph. If the area is positive, the displacement is positive, indicating movement in the positive direction. If the area is negative, the displacement is negative, indicating movement in the negative direction.

By following these steps, you can accurately calculate the displacement from a velocity-time graph. Remember to carefully interpret the graph's characteristics and consider the sign of the areas to determine the direction of displacement.

The area under the velocity time graph is equal to the displacement