A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 25 mi along the highway. When the car reached the location of the second officer 19 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the60 mi/hr speed limit. Why can the officer conclude that the driver exceeded the speed limit? How fast must the car have been traveling?

Question
Asked Oct 22, 2019
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A state patrol officer saw a car start from rest at a highway on-ramp. She radioed ahead to another officer 25 mi along the highway. When the car reached the location of the second officer 19 min later, it was clocked going 60 mi/hr. The driver of the car was given a ticket for exceeding the60 mi/hr speed limit. Why can the officer conclude that the driver exceeded the speed limit? How fast must the car have been traveling?

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Expert Answer

Step 1

known fact:

The speed is calculated as the ratio of the distance with time.
Mean value theorem
If f(x) is continuous on the closed interval a,b and differentiable on the
open interval (a,b), then there exists some value x = c such that
re) - f(b)-1(a)]
(b-a)
f(c)
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Image Transcriptionclose

The speed is calculated as the ratio of the distance with time. Mean value theorem If f(x) is continuous on the closed interval a,b and differentiable on the open interval (a,b), then there exists some value x = c such that re) - f(b)-1(a)] (b-a) f(c)

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Step 2

Find why can the officer conclude that the driv...

By mean value theorem, if the average speed is greater than the speed limit,
then at some point we must have exceeded the speed limit
In order to answer the question, if the driver exceeded the speed limit or not.
Calculate the average speed:
25 0
The average speed-
19
0
60
=78.95 mi/h
Thus, the driver exceeded the speed limit
help_outline

Image Transcriptionclose

By mean value theorem, if the average speed is greater than the speed limit, then at some point we must have exceeded the speed limit In order to answer the question, if the driver exceeded the speed limit or not. Calculate the average speed: 25 0 The average speed- 19 0 60 =78.95 mi/h Thus, the driver exceeded the speed limit

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Math

Calculus