A student observes a speed-time graph for a car that moves with constant speed for 10 seconds, then accelerates for 5 seconds. How can the student use the graph to calculate the total distance travelled during these 15 seconds?
By calculating the area under the speed-time graph for each section and adding them
On a speed–time graph, the distance travelled during any interval is equal to the area under the curve for that interval, because distance = speed × time and area is exactly that product.
Here the motion has two clearly different phases: the first 10 seconds at constant speed and the next 5 seconds while accelerating. The correct approach is to find the area under the graph for the constant-speed portion (a rectangle) and the area for the accelerating portion (a trapezium or triangle) and then add the two areas. Using only the acceleration portion ignores the first 10 s of distance. Multiplying the final speed by the total time overestimates the distance because the car was slower earlier. Multiplying the total time by the “average speed shown on the graph” is essentially the area method, but only if the average is computed correctly — the safe and general method is adding areas.
Hence, the answer is By calculating the area under the speed-time graph for each section and adding them.
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