An athlete runs a 100 m race in 12.5 s. Explain why, for part of the race, the athlete must have been running faster than the speed calculated in (a).
GCE O-level 5052 Science (Physics) 2004 November Paper 2 Question 1(b)
Proof: Consider the area under an arbitrary speed-time graph that starts from rest and the area under another speed-time graph that is travelling at a constant speed, which is equal to the maximum speed of the first graph. Both graphs stop at time t. Thus, the area under the first speed-time graph = average speed x t while the area under the second speed-time graph = maximum speed x t. Since first area < second area, hence average speed < maximum speed.
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