Derivative as a Rate of Change Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Let be the position function of a body moving on a coordinate line, with in meters and in seconds. (a) Find the body's displacement and average velocity for the time interval (b) Find the body's speed and acceleration at the endpoints of the time interval (c) When, if ever, during the time interval does the body change direction?

(2) Let be the position function of a body moving on a coordinate line, with in meters and in seconds. (a) Find the body's displacement and average velocity for the time interval (b) Find the body's speed and acceleration at the endpoints of the time interval (c) When, if ever, during the time interval does the body change direction?

(3) (a) Let be the position function of a body moving on a coordinate line, with in meters and in seconds. (b) Find the body's displacement and average velocity for the time interval (c) Find the body's speed and acceleration at the endpoints of the time interval When, if ever, during the time interval does the body change direction?

(4) (a) Let be the position function of a body moving on a coordinate line, with in meters and in seconds. (b) Find the body's displacement and average velocity for the time interval (c) Find the body's speed and acceleration at the endpoints of the time interval When, if ever, during the time interval does the body change direction?

(5) At time the position of a body moving along the -axis is (a)Find the body's acceleration each time the velocity is zero. (b) Find the body's speed each time the acceleration is zero. (c) Find the total distance travelled by the body from to

(6) A rock is thrown vertically upward from the surface of the moon at a velocity of 24 m/se (about 86 km/h) reaches a height of meters in sec. (a) Find the rock's velocity and acceleration at time (b) How long does it take the rock to reach its highest point? (c) How high does the rock go? (d) How long does it take the rock to reach half its maximum height?

(7) Had Galileo dropped a cannonball from the Tower of Pisa, 179 ft above the ground, the ball's height above the ground sec into the fall would have been (a) What would have been the ball's velocity, speed, and acceleration at time (b) About how long would it have taken the ball to hit the ground? (c) What would have been the balls velocity at the moment of impact?

(8) The number of gallons of water in a tank minutes after the tank has started to drain is How fast is the water running out at the end 19 min? What is the average rate at which the water flows out during the first 10 minutes?

(9) Suppose that the distance an aircraft travels along a runway before takeoff is given by where is measured in meters from the starting point an is measured in seconds from the time the brakes are released. The aircraft will become airborne when its speed reached 200 km/h. How long will it take to become airborne, and what distance will it travel to that time?

(10) Suppose that the dollar cost of producing washing machines is

    (a) Find the average cost per machine of producing the first 100 washing machines.
    (b) Find the marginal cost when 100 washing machines are produced.
    (c) Show that the marginal cost when 100 washing machines are produced is approximately the cost of producing one more washing machine after the first 100 have been made, by calculating the latter cost directly.

(11) Suppose the revenue from selling washing machines is

dollars.

    (a) Find the marginal revenue when 100 machines are produced.
    (b) Use the function to estimate the increase in revenue that will result from increasing production from 100 machines a week to 101 machines a week.
    (c) Find the limit of a How would you interpret this number?

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Derivative As A Rate Of Change Homework
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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