A common example of the use of areas is when interpreting a graph of motion. You will know that an object’s average speed multiplied by the time it was in motion tells you the distance travelled by the object. On a speed/time graph, the area under the line represents the product of speed and time, hence the distance travelled.
Figure 1 is a speed-time graph for something travelling with uniform acceleration a, having an initial speed u and reaching a speed v after a time interval t. To calculate the area under the line, you can treat it either as a rectangle plus a right-angled triangle, or as a trapezium. Let us look at these shapes.
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