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Originally Posted by Chas H
If Ah-Kay made a mistake, how did he come to the correct answer?
There is no graph of any sort to consider just the simple case posed by the OP.
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His answer is only correct if the vehicle has constant acceleration. In that case, a graph of velocity versus time is a straight line with a slope equal to the acceleration. The distance traveled is the area under the curve (i.e. the integral with respect to time.) The area under the linear curve is equal to the area under a curve that has a constant velocity of 50. Draw it and you will see. Then draw a velocity curve that is steep at the beginning and tapering off at the end. The area under that curve will be greater than the area under the linear curve. That result stands to reason because the car with the quicker acceleration at the beginning will spend more of its time traveling at high speed, even though it will not continue to gain speed as quickly as the other car will at the end of the trip.
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...Averaging the speed is perfectly valid in this case.
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That's true
only if acceleration is constant.