How can displacement be determined from a velocity-time graph?

Displacement can be determined from a velocity-time graph by calculating the area under the graph. This is because the area between the velocity line and the time axis represents the distance covered during that time interval, and since the velocity is a vector quantity, this area also reflects the direction and magnitude of the displacement.

When analyzing a velocity-time graph, the area can be computed by breaking it into geometric shapes, such as rectangles and triangles, and summing those areas. For example, if a velocity is constant, the area will be a rectangle defined by the height (velocity) and width (time). If the velocity changes, the area can be found using trapezoids or triangles depending on the shape of the graph. The total area gives the overall displacement, which can be positive or negative based on the direction of velocity.

This relationship emphasizes the integral nature of displacement in physics, where the integral of velocity over time directly tells us how far an object has traveled from its initial position, accounting for any changes in direction.