How to calculate displacement from a velocity-time graph?

You calculate displacement from a velocity-time graph by finding the area under the curve.

In a velocity-time graph, the displacement of an object is represented by the area under the graph line. This is because the area under the graph line is equal to the product of velocity and time, which is the definition of displacement.

To calculate the displacement, you need to find the area under the graph line. If the graph line is a straight line, this can be done by calculating the area of the geometric shape formed by the graph line and the axes. For example, if the graph line forms a rectangle with the axes, the area (and therefore the displacement) is calculated by multiplying the length (time) by the height (velocity). If the graph line forms a triangle, the area is calculated by multiplying the base (time) by the height (velocity) and dividing by two.

If the graph line is a curve, the area under the curve can be approximated by dividing the area into small rectangles or trapezoids, calculating the area of each, and adding them together. This method is known as numerical integration.

Remember, the area under the curve can be above or below the time axis. If it's above, the displacement is positive, indicating movement in the positive direction. If it's below, the displacement is negative, indicating movement in the opposite direction.

In summary, to calculate displacement from a velocity-time graph, find the area under the graph line. This can be done by calculating the area of the geometric shape formed by the graph line and the axes, or by using numerical integration if the graph line is a curve.