If a rock is thrown upward on the Moon with an initial velocity of 43 meters per second and from initial heightof 1.8 meters, then its height, in meters, t seconds later is given by the function h(t) = 1.8+43t - 0.81t²A. Determine the average velocity of the rock over the time interval [3, 3.5]. Input the numerical value.Include appropriate units on paper.Average velocity over [3, 3.5] :B. Using successively smaller time intervals, estimate the instantaneous velocity of the rock at t = 3.Input the numerical value. Include appropriate units on paper.Instantaneous velocity at t = 3:

If f(t) is the position function then the average velocity over [a,b] is.

Answered: If a rock is thrown upward on the Moon…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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128t A. What is the average velocity of the ball over the time intervals? a. [2, 3] b. [2, 2.5] c. [2. 2.1] B. What is the instantaneous velocity at time t= 2? C. What is the instantaneous velocity at time t=5? Is the ball rising or falling? D. When will the ball hit the ground? 4. An object is dropped from a certain height. It is known that it will fall a distance s, in feet, in t seconds, given by s(1) = -161? A. How far will it fall in 3 sec? B. How far will it fall in 5 sec? C. What is the average rate of change of distance with respect to time during the period from 3 to 5 sec? (This is also average velocity). 5. During the construction of a high-rise building, a worker accidentally dropped his portable electric screwdriver from a height of 400 ft. After t seconds, the screwdriver had fallen a di
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An object is dropped straight down from a helicopter. The object falls faster and faster but its acceleration (rate of change of its velocity) decreases over time because of air resistance. The acceleration is measured in ft/sec² and recorded every second after the drop for 5 sec, as shown. Find the following estimates. to 1 2 3 4 5 a 32.00 19.41 11.77 7.14 4.33 2.63 a. Find an upper estimate for the speed when t = 5. ft/sec b. Find a lower estimate for the speed when t = 5. ft/sec c. Find an upper estimate for the distance fallen when t = 3. ft
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1. A tennis ball is dropped from the top of a building that is 1545 feet tall, with an initial velocity of -30.5 feet per second. Use the position function s(t)=-16t^2+v0t+s0 to help you answer the given questions. a.Write the equations of the position and instantaneous velocity functions. b. What is the average velocity over the first two seconds? c.When does the coin hit the ground? Round your answer to two decimal places. d.What is the velocity of the coin upon impact? 2.find all the values of x for which f(x) will have a horizontal tangent line f(x)=(x-4)/(x^2-7) 3. Find the derivative of the function. g(x)=4x(3x+2)^5 4.

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