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 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. <IMAGE>
a. Determine the average velocity of the car during the first 45 minutes of the trip.

Verified step by step guidance

1. Convert the time of 45 minutes into hours, which is 0.75 hours.
2. Identify the position function s = f(t) that describes the car's location in miles at time t hours after 9:00 A.M.
3. Calculate the position of the car at t = 0 (which is 9:00 A.M.) and at t = 0.75 (which is 9:45 A.M.) using the position function.
4. Use the formula for average velocity, which is given by the change in position divided by the change in time: average velocity = (f(0.75) - f(0)) / (0.75 - 0).
5. Substitute the values obtained from the position function into the average velocity formula to find the average velocity during the first 45 minutes.