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Math Calculus Calculus of a Single Variable

Motion Along a Line In Exercises 81-84, the function s ( t ) describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time t ≥ 0 . (b) Identify the time interval (s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction. s ( t ) = t 3 − 20 t 2 + 128 t − 280

Motion Along a Line In Exercises 81-84, the function s ( t ) describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time t ≥ 0 . (b) Identify the time interval (s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction. s ( t ) = t 3 − 20 t 2 + 128 t − 280

Solution Summary: The author explains that the speed function can be computed by differentiating the function for distance with respect to time.

Calculus of a Single Variable

Calculus of a Single Variable

11th Edition

ISBN: 9781337275361

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Textbook Question

Chapter 3.3, Problem 84E

Motion Along a Line In Exercises 81-84, the function s ( t )

describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time t ≥ 0

. (b) Identify the time interval (s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction.

s ( t ) = t 3 − 20 t 2 + 128 t − 280

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Chapter 3.3, Problem 83E

Chapter 3.3, Problem 85E

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Calculus of a Single Variable

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Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Finding Numbers In Exercises 510, find two...Ch. 3.7 - Prob. 10E Ch. 3.7 - Maximum Area In Exercises 11 and 12, find the...Ch. 3.7 - Prob. 12E Ch. 3.7 - Minimum Perimeter In Exercises 13 and 14, find the...Ch. 3.7 - Prob. 14E Ch. 3.7 - Minimum Distance In Exercises 15 and 16, find the...Ch. 3.7 - Minimum Distance In Exercises 15 and 16, find the...Ch. 3.7 - Minimum Area A rectangular poster is to contain...Ch. 3.7 - Minimum Area A rectangular page is to contain 36...Ch. 3.7 - Minimum Length A farmer plans to fence a...Ch. 3.7 - Maximum Volume A rectangular solid (with a square...Ch. 3.7 - Maximum Area A Norman window is constructed by...Ch. 3.7 - Maximum Area A rectangle is bounded by the x- and...Ch. 3.7 - Minimum Length and Minimum Area A right triangle...Ch. 3.7 - Maximum Area Find the area of the largest...Ch. 3.7 - Maximum Area A rectangle is bounded by the x-axis...Ch. 3.7 - Prob. 26E Ch. 3.7 - Numerical, Graphical, and Analytic Analysis An...Ch. 3.7 - Prob. 28E Ch. 3.7 - Maximum Volume A rectangular package to be sent by...Ch. 3.7 - Maximum Volume Rework Exercise 29 for a...Ch. 3.7 - Prob. 31E Ch. 3.7 - Prob. 32E Ch. 3.7 - Prob. 33E Ch. 3.7 - Minimum Cost An industrial tank of the shape...Ch. 3.7 - Minimum Area The sum of the perimeters of an...Ch. 3.7 - Maximum Area Twenty feet of wire is to be used to...Ch. 3.7 - Beam Strength A wooden beam has a rectangular...Ch. 3.7 - Prob. 38E Ch. 3.7 - Minimum Cost An offshore oil well is 2 kilometers...Ch. 3.7 - Illumination A light source is located over the...Ch. 3.7 - Minimum Time A man is in a boat 2 miles from the...Ch. 3.7 - Prob. 42E Ch. 3.7 - Prob. 43E Ch. 3.7 - Prob. 44E Ch. 3.7 - Prob. 45E Ch. 3.7 - Numerical, Graphical, and Analytic Analysis The...Ch. 3.7 - Prob. 47E Ch. 3.7 - Prob. 48E Ch. 3.7 - Prob. 49E Ch. 3.7 - Prob. 50E Ch. 3.7 - Prob. 51E Ch. 3.7 - Maximum Area Consider a symmetric cross inscribed...Ch. 3.7 - Minimum Distance Find the point on the graph of...Ch. 3.7 - Prob. 54E Ch. 3.7 - Prob. 55E Ch. 3.7 - Prob. 56E Ch. 3.8 - Prob. 1E Ch. 3.8 - Failure of Newtons Method Why does Newtons Method...Ch. 3.8 - Prob. 3E Ch. 3.8 - Prob. 4E Ch. 3.8 - Prob. 5E Ch. 3.8 - Prob. 6E Ch. 3.8 - Prob. 7E Ch. 3.8 - Prob. 8E Ch. 3.8 - Prob. 9E Ch. 3.8 - Prob. 10E Ch. 3.8 - Prob. 11E Ch. 3.8 - Prob. 12E Ch. 3.8 - Prob. 13E Ch. 3.8 - Prob. 14E Ch. 3.8 - Prob. 15E Ch. 3.8 - Prob. 16E Ch. 3.8 - Prob. 17E Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Points of Intersection In Exercises 17-20, apply...Ch. 3.8 - Prob. 20E Ch. 3.8 - Prob. 21E Ch. 3.8 - Prob. 22E Ch. 3.8 - Prob. 23E Ch. 3.8 - Failure of Newton's Method In Exercises 23 and 24,...Ch. 3.8 - Prob. 25E Ch. 3.8 - Prob. 26E Ch. 3.8 - Prob. 27E Ch. 3.8 - Prob. 28E Ch. 3.8 - Prob. 29E Ch. 3.8 - Using Newtons Method Exercises 29-31 present...Ch. 3.8 - Prob. 31E Ch. 3.8 - Prob. 32E Ch. 3.8 - Prob. 33E Ch. 3.8 - Prob. 34E Ch. 3.8 - Prob. 35E Ch. 3.8 - Prob. 36E Ch. 3.8 - Prob. 37E Ch. 3.8 - Prob. 38E Ch. 3.8 - Prob. 39E Ch. 3.8 - Prob. 40E Ch. 3.8 - Prob. 41E Ch. 3.8 - Prob. 42E Ch. 3.9 - Prob. 1E Ch. 3.9 - Prob. 2E Ch. 3.9 - Prob. 3E Ch. 3.9 - Prob. 4E Ch. 3.9 - Using a Tangent Line Approximation In Exercises...Ch. 3.9 - Prob. 6E Ch. 3.9 - Prob. 7E Ch. 3.9 - Prob. 8E Ch. 3.9 - Prob. 9E Ch. 3.9 - Prob. 10E Ch. 3.9 - Prob. 11E Ch. 3.9 - Prob. 12E Ch. 3.9 - Prob. 13E Ch. 3.9 - Prob. 14E Ch. 3.9 - Prob. 15E Ch. 3.9 - Prob. 16E Ch. 3.9 - Prob. 17E Ch. 3.9 - Prob. 18E Ch. 3.9 - Prob. 19E Ch. 3.9 - Prob. 20E Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Prob. 22E Ch. 3.9 - Prob. 23E Ch. 3.9 - Prob. 24E Ch. 3.9 - Finding a Differential In Exercises 1928, find the...Ch. 3.9 - Prob. 26E Ch. 3.9 - Prob. 27E Ch. 3.9 - Prob. 28E Ch. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 29 and 30, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Using Differentials In Exercises 31 and 32, use...Ch. 3.9 - Prob. 33E Ch. 3.9 - Area The measurements of the base and altitude of...Ch. 3.9 - Prob. 35E Ch. 3.9 - Prob. 36E Ch. 3.9 - Stopping Distance The total stopping distance T of...Ch. 3.9 - Prob. 38E Ch. 3.9 - Pendulum The period of a pendulum is given by...Ch. 3.9 - Prob. 40E Ch. 3.9 - Projectile Motion The range R of a projectile is...Ch. 3.9 - Prob. 42E Ch. 3.9 - Prob. 43E Ch. 3.9 - Prob. 44E Ch. 3.9 - Prob. 45E Ch. 3.9 - Approximating Function Values In Exercises 4346,...Ch. 3.9 - Prob. 47E Ch. 3.9 - Prob. 48E Ch. 3.9 - Prob. 49E Ch. 3.9 - Prob. 50E Ch. 3.9 - True or False? In Exercises 4953, determine...Ch. 3.9 - Prob. 52E Ch. 3.9 - Prob. 53E Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Finding Extrema on a Closed Interval In Exercises...Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Using Rolle's Theorem In Exercises 9-12, determine...Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Maximum Area A rancher has 400 feet of fencing...Ch. 3 - Prob. 82RE Ch. 3 - Minimum Length A right triangle in the first...Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Prob. 87RE Ch. 3 - Prob. 88RE Ch. 3 - Prob. 89RE Ch. 3 - Prob. 90RE Ch. 3 - Prob. 91RE Ch. 3 - Prob. 92RE Ch. 3 - Prob. 93RE Ch. 3 - Prob. 94RE Ch. 3 - Prob. 95RE Ch. 3 - Prob. 96RE Ch. 3 - Prob. 97RE Ch. 3 - Prob. 98RE Ch. 3 - Prob. 99RE Ch. 3 - Prob. 100RE Ch. 3 - Prob. 101RE Ch. 3 - Prob. 1PS Ch. 3 - Prob. 2PS Ch. 3 - Relative Minimum Let f(x)=cx+x2 Determine all...Ch. 3 - Prob. 4PS Ch. 3 - Prob. 5PS Ch. 3 - Illumination The amount of illumination of a...Ch. 3 - Prob. 7PS Ch. 3 - Areas of Triangles The line joining P and Q...Ch. 3 - Mean Value Theorem Determine the values a, b, and...Ch. 3 - Mean Value Theorem Determine the values a. b, c....Ch. 3 - Prob. 11PS Ch. 3 - Proof (a) Prove that limxx2= (b) Prove that...Ch. 3 - Prob. 13PS Ch. 3 - Prob. 14PS Ch. 3 - Prob. 15PS Ch. 3 - Prob. 16PS Ch. 3 - Prob. 17PS Ch. 3 - Prob. 18PS Ch. 3 - Prob. 19PS

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A person lights the fuse on a model rocket and starts to move away from the rocket at a rate of 3ft/sec. Five seconds after lightning the fuse the rocket launches straight up into the air at a rate of 10ft/sec. Is the distance between the person and the rocket increasing or decreasing (a) 6 seconds after launch and (b) 12 seconds after launch?
Data collected by PH210 students to describe the motion of a person on an amusement park water slide who moved from a level section of the slide onto a smooth slope at t= 0 seconds is described in thefollowing data. t(sec) 0.50 0.01 7.10 0.20 0.75 0.01 7.90 0.20 1.00 0.01 8.50 0.40 1.25 0.01 9.50 0.30 1.50 0.01 10.00 0.40 1.75 0.01 10.50 0.40 2.00 0.01 11.20 0.30 If we assume that the velocity data can be fitted by the linear equation: Ut) = v, + at¸ we can determine the initial velocity U, and the acceleration a of the person. Use your Excel Template or least squares fitting table from the previous lecture to answer the following questions. Carry at least two extra decimal places through all statistical calculations, and round appropriately when expressing the final results. %3D Find N-2 mx, Select one: O a. 0.0209 O b. 0.0109 O c. 0.0409 O d. 0.0309 O e. none of these

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