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Flashcards in Chapter 7 Practice Test Deck (20):

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?



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?



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.



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.



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


A piece of wire 20 in. long is cut into two pieces, and each piece is bent into the shape of a square. What should the lengths of the two pieces be if the sum of the areas of the two squares is a minimum?

10 in. and 10 in.


Given: f(x)=4/x^2Find:f′′(−2)



Determine d2/dx2[e^3x].



Given f(x)=sin(x) and g(x)=f′(x)+f′′(x)+f′′′(x)+f(4)(x),evaluate g(π6).



Use linear approximation with x0=π/4 to estimate the value of tan 7π/24correct to two decimal places.


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