1. A ball is thrown directly upward. Its height h (in feet) above the ground after t seconds is given by h (t) = 22 + 80t - 16t 2. How long after it is thrown is the ball falling at 48 ft /?sec?
2. Given the position function p (t) = t 2 - 4t + 3, find the velocity function, v (t).
3. An object is hurled directly upward. Its height h (in feet) above ground level after t seconds is given by h (t) = 112t - 16t2. Find its velocity the first time its height is 160 ft.
4. An object is hurled directly upward. Its height h (in feet) above ground level after t seconds is given by h (t) = 112t - 16t 2. Find the height when the velocity is -80 ft /?sec.
5. Given the function p(t)= 1/3x3 - 4x2 + 2x + 5 find the velocity function , v(t) and the acceleration a (t).
6. Aparticle moves along the x -axis, with its position, x, given by x(t) = t2 + 16/t - 20 at what time the velocity of the particle equal to 0?
7. A baseball diamond has the shape of a square with sides 90 feet long. A player is running from second to third at a speed of 28 ft /?sec. At the time he is 30 feet from third, what is the rate of change of his distance from the home plate?
8. A pebble is dropped into a small pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a rate of 1 foot per second. When this radius is 4 feet, at what rate is the total area of the disturbed water increasing?
9. The area of a circle is increasing at a rate of 24 in2 /?min. What is the rate of change of the radius at the instant that the radius is 6 in?
10. A stone is dropped into a still pond. Concentric circular ripples spread out and the radius of the disturbed area increases at a rate of 16 cm /?sec. At what rate does the area of the disturbed region increase when its radius is 4 cm?
11. A ladder 25 ft long is leaning against the side of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top moving down the wall when the base of the ladder is 7 feet from the wall?
12. A 16 foot plank is leaning on the side of a wall and is being pulled up the wall at a rate of 1/2 ft /?sec by a worker on top of the wall. How fast is the end of the plank sliding along the ground when it is 8 feet from the wall?
13. An airplane is flying at an altitude of 6 miles and passes over a radar antenna. The rate of change of the distance between the plane and the antenna is 240 miles per hour when the distance between the plane and the antenna is 10 miles. What is the speed of the plane?
14. A kite is flying at a height of 40 feet. A child is flying it so that it is moving horizontally at a rate of 3 ft /?sec. If the string is taut, at what rate is the string being let out when the amount of string released is 50 feet?
15. Two cars, one going due east at 25 m /?sec and the second going due south at 50/3 m /?sec are traveling toward the intersection of the two roads they are driving on. At what rate are the two cars approaching each other at the instant when the first car is 200 m and the second car is 150 m from the intersection?
16. A balloon is being inflated from a helium tank at a constant rate of 50 cubic inches per minute. How fast is the radius of the balloon increasing when the radius is 5 inches? Assume that the balloon is a perfect sphere.