Position (miles from station)40-30-2010-10-<-20-300.51.0 1.5s= f(t)2,0 25 3.0Time (hours)1 11. Highway travel A state patrol station is located on a straight north-southfreeway. A patrol car leaves the station at 9:00 A.M. heading north withf(t) that gives its location in miles t hours after 9:00A.M. (see figure). Assume s is positive when the car is north of the patrolstation.position function s=a. Determine the average velocity of the car during the first 45 minutesof the trip.b. Find the average velocity of the car over the interval [0.25, 0.75]. Isthe average velocity a good estimate of the velocity at 9:30 A.M.?c. Find the average velocity of the car over the interval [1.75, 2.25].Estimate the velocity of the car at 11:00 A.M. and determine thedirection in which the patrol car is moving.d. Describe the motion of the patrol car relative to the patrol stationbetween 9:00 A.M. and noon.

After of initial trip, the car is away from the patrol station. So, the total displacement is 30…

Answered: A.M. (see figure). sitive when the car…

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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Related questions

Question

Position (miles from station)
40-
30-
20
10
-10-
<-20
-30
0.5
1.0 1.5
s
= f(t)
2,0 25 3.0
Time (hours)
1

11. Highway travel A state patrol station is located on a straight north-south
freeway. A patrol car leaves the station at 9:00 A.M. heading north with
f(t) that gives its location in miles t hours after 9:00
A.M. (see figure). Assume s is positive when the car is north of the patrol
station.
position function s
=
a. Determine the average velocity of the car during the first 45 minutes
of the trip.
b. Find the average velocity of the car over the interval [0.25, 0.75]. Is
the average velocity a good estimate of the velocity at 9:30 A.M.?
c. Find the average velocity of the car over the interval [1.75, 2.25].
Estimate the velocity of the car at 11:00 A.M. and determine the
direction in which the patrol car is moving.
d. Describe the motion of the patrol car relative to the patrol station
between 9:00 A.M. and noon.

Expert Solution

Step 1: Compute the average velocity.

After $45 space text minutes end text equals 0.75 space text hours end text$ of initial trip, the car is $s equals f left parenthesis 0.75 right parenthesis space equals 30 space text miles end text$ away from the patrol station. So, the total displacement is 30 miles in 0.75 hours.

Thus, $text average velocity= end text fraction numerator text total displacement end text over denominator text total time end text end fraction equals fraction numerator 30 over denominator 0.75 end fraction text miles/hour end text equals 40 text miles/hour end text$