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 loca tion 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. an 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. 40 30 s = f(1) 20 10- 0,5 1.0 15 20 2,5 3,0 10 -20- -30 Time (hours) Position (miks from station)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.