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>
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.

Velocity of a car The graph shows the position s=f(t) of a car t hours after 5:00 P.M. relative to its starting point s=0,where s is measured in miles. <IMAGE>

b. At approximately what time is the car traveling the fastest? The slowest?

Throwing a stone Suppose a stone is thrown vertically upward from the edge of a cliff on Earth with an initial velocity of 32 ft/s from a height of 48 ft above the ground. The height (in feet) of the stone above the ground t seconds after it is thrown is s(t) = -16t²+32t+48.

c. What is the height of the stone at the highest point?

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.

Airline travel The following figure shows the position function of an airliner on an out-and-back trip from Seattle to Minneapolis, where s = f(t) is the number of ground miles from Seattle t hours after take-off at 6:00 A.M. The plane returns to Seattle 8.5 hours later at 2:30 P.M. <IMAGE>

a. Calculate the average velocity of the airliner during the first 1.5 hours of the trip (0 ≤ t ≤ 1.5).

Airline travel The following figure shows the position function of an airliner on an out-and-back trip from Seattle to Minneapolis, where s = f(t) is the number of ground miles from Seattle t hours after take-off at 6:00 A.M. The plane returns to Seattle 8.5 hours later at 2:30 P.M. <IMAGE>

d. Determine the velocity of the airliner at noon (t = 6) and explain why the velocity is negative.

{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity in m/s is given by v(t) = 200e^−t/10, for t≥0.

a. Graph the velocity function, for t≥0.

{Use of Tech} Decreasing velocity A projectile is fired upward, and its velocity (in m/s) is given by v(t) = 200 / √t+1, for t≥0.

a. Graph the velocity function, for t≥0.

Motion Along a Coordinate Line

Exercises 1–6 give the positions s = f(t) of a body moving on a coordinate line, with s in meters and t in seconds.

a. Find the body’s displacement and average velocity for the given time interval.

s = (t⁴/4) − t³ + t², 0 ≤ t ≤ 3