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Kevin runs a race in his hometown

Kevin runs a race in his hometown

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Kevin runs a race in his hometown. His buddy…
Kevin runs a race in his hometown. His buddy Bill rides behind him on a bike and clocks his speed every 15 minutes. Kevin starts out strong, but after an hour and a half he is very tired and decides to call it quits. Bill has the following data for the run: Time (since start (min) Speed (mph) 0 12 15 11 30 10 45 10 60 8 75 7 90 0 (a) Assuming Kevin's speed is never increasing give upper and lower estimates for the distance Kevin ran during the first half hour. (b) Give upper and lower estimates for the distance Kevin ran in total for the entire hour and a half. 4
Transcribed Image Text:Kevin runs a race in his hometown. His buddy Bill rides behind him on a bike and clocks his speed every 15 minutes. Kevin starts out strong, but after an hour and a half he is very tired and decides to call it quits. Bill has the following data for the run: Time (since start (min) Speed (mph) 0 12 15 11 30 10 45 10 60 8 75 7 90 0 (a) Assuming Kevin's speed is never increasing give upper and lower estimates for the distance Kevin ran during the first half hour. (b) Give upper and lower estimates for the distance Kevin ran in total for the entire hour and a half. 4
Expert Solution
Step 1
Time (since start (in min)) 0 15 30 45 60 75 90
Time (in hours) 0 14 12 34 1 54 32
Speed (mph) 12 11 10 10 8 7 0

 

(a)

For First half hour:

∆x = 14-0 = 14

(i)

So, Lower estimate = ∆x f(to) + f(t1)

Lower estimate = 14f(0) + f14 

Lower Estimate = 0.25 * (12 + 11)

Lower Estimate = 5.75

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