How do you interpret the area under a speed-time graph?

The area under a speed-time graph represents the distance travelled by an object.

When you look at a speed-time graph, the x-axis typically shows time, while the y-axis shows speed. The area under the curve of this graph gives you the total distance travelled over the given time period. This is because distance is the product of speed and time, and the area under the graph essentially sums up all these small products over the entire duration.

To calculate the area, you might need to break it down into simpler shapes like rectangles, triangles, or trapeziums, especially if the graph is not a simple straight line. For example, if the graph is a straight horizontal line, the area is simply the speed multiplied by the time. If the graph forms a triangle, you would use the formula for the area of a triangle (1/2 * base * height), where the base is the time and the height is the speed.

In more complex cases, where the graph has curves or multiple segments, you might need to add up the areas of several different shapes. This method is known as integration in higher-level maths, but at the GCSE level, you can usually manage with basic geometric shapes.

Understanding this concept is crucial because it allows you to interpret real-world scenarios, such as calculating how far a car has travelled over a certain period, given its speed at different times. This skill is not only useful in exams but also in everyday life situations.