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 position function s = 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.

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.

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40 30 s = f(t). 10 2,5 0,5 10 3.0 1,5 - 10 - 20 – 30 Time (hours) Position (miles from station) 20