Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 20: 14


They All Finished (the curves all reached 100m on the y-axis): First: A Second: B Third: C What this graph tells us: - A had a slow initial acceleration, which increases along its path, hence a greater top seed which is able to place 1st - B had the fastest initial acceleration but slowed down and came to a stop somewhere in the middle of the race hence their 2nd place. - C Had the second greatest initial acceleration, which decreases along the middle and increases again a bit at the end, coming 3rd.

Work Step by Step

It is relatively straightforward to determine who came first, by looking at which point at y = 100m has the lowest x-value (meaning they finish in the lowest time), and that is A. Looking at the graph of A, the line curved up, which indicated that A was accelerating, and the top speed can be determined by the gradient at ~10s, which was the steepest point, and hence the highest rise/run or m/s. This top speed was higher than the curve C, and was enough to surpass C at ~11s. However, we cannot tell (without values) if the top speed of A was higher than the top speed of B, but because B stopped during the 3-15s period (as the gradient was a constant 0 {hence 0 m/s}), A was still able to surpass the graph of B when it was stationary. This is just a mere explanation using Calculus - but the observations can still be determined by just studying the graph logically.
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