How to calculate total distance travelled using a velocity-time graph?

The total distance travelled can be calculated from a velocity-time graph by finding the area under the graph.

In a velocity-time graph, the velocity of an object is plotted against time. The total distance travelled by the object is represented by the area under the graph. This is because the area under the graph is equal to the product of velocity and time, which gives the distance travelled.

To calculate the total distance travelled, you need to divide the graph into different shapes such as rectangles, triangles, or trapezoids, depending on the shape of the graph. Then, calculate the area of each shape and add them together to get the total distance.

For example, if the graph is a straight line, you can divide it into a rectangle and a triangle. The area of the rectangle is length times width, which is velocity times time. The area of the triangle is half the base times the height, which is half the time times the change in velocity. Add these two areas together to get the total distance travelled.

If the graph is a curve, you can approximate it by dividing it into small rectangles and adding up their areas. The more rectangles you use, the more accurate your approximation will be.

Remember, if the graph goes below the time axis, this indicates that the object is moving in the opposite direction. You should still calculate the area of this part of the graph, but it will subtract from the total distance travelled, not add to it.

In summary, to calculate the total distance travelled using a velocity-time graph, find the area under the graph by dividing it into shapes, calculating the area of each shape, and adding them together.