Chapter 7 Practice Test Flashcards
A particle moves along the x-axis with its position at time t given by p(t)=t+√t. Which of the following is the velocity at time t=9?
7/6
A particle moves along the x-axis, with its position, x, given by x(t)=t^2+16/t−20. At which of the following times is the velocity of the particle equal to 0?
2
A point moves along the x-axis, with its position, x, at time t > 0 given by
x (t) = t ^3 − 12t ^2 + 45t − 50.
For which of the following values of t is the point momentarily at rest (motionless)?
t = 3 and t = 5
Given the position function p (x) = e^ 2x, find the acceleration function.
4e^2x
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?
4 sec
True or false?
The velocity with which an object is thrown upward from ground level is equal to the velocity with which it strikes the ground. Ignore air resistance.
false
A car traveling at a rate of 30 ft / sec is approaching an intersection. When the car is 120 ft from the intersection, a truck traveling at a rate of 40 ft / sec crosses the intersection. If the roads are at right angles to each other, how fast are the car and the truck separating 2 seconds after the truck crosses the intersection?
14 ft / sec
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?
−28√10 ft/sec
A man 6 feet tall is walking toward a building at the rate of 5 ft / sec. If there is a light on the ground 50 ft from the building, how fast is the man’s shadow on the building growing shorter when he is 30 ft from the building?
−15/4 ft/sec
A man 6 feet tall walks at a rate of 5 ft / sec away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the length of his shadow changing?
10/3 ft/sec
An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate at which the angle of elevation is changing when the angle is π / 6.
30 rad / hr
A 15 foot ladder is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 ft / sec. Find the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall.
21/4 ft^2/sec
A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in.
1/9 in/min
In order for a rectangular solid package to be mailed, the sum of the height and the perimeter of the base cannot exceed 108 in. If the base of a package is a square, what is the length of the side of the square that would maximize the volume of the package?
18 in
A physical fitness room consists of a rectangular region with a semicircle at each end. If the perimeter of the room is to be a 200 ft running track, what is the radius of the semicircle that will make the area of the rectangular region a maximum?
50/π ft
