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Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity v, so that du/dt = -kv2. Show that vo v(t) = 1+ vokt and that 1 In(1 + vokt). k x(t) = xo + , Note that, in contrast with the result of Problem 2, x(t) +o as t → +oo. Which offers less resistance when the body is moving fairly slowly-the medium in this prob- lem or the one in Problem 2? Does your answer seem consistent with the observed behaviors of x(t) as t → o?

Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity v, so that du/dt = -kv2. Show that vo v(t) = 1+ vokt and that 1 In(1 + vokt). k x(t) = xo + , Note that, in contrast with the result of Problem 2, x(t) +o as t → +oo. Which offers less resistance when the body is moving fairly slowly-the medium in this prob- lem or the one in Problem 2? Does your answer seem consistent with the observed behaviors of x(t) as t → o?

Calculus: Early Transcendentals
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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Problem 2: (Reference only) x(t)=xo+(vo/k)(1-e^-kt)

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4. Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity v, so that dv/dt = -kv². Show that %3D v(t) : 1+ vokt h01 and that 1 x(t) = xo + In(1 + vokt). k Note that, in contrast with the result of Problem 2, x(t) –→ +o as t → +o. Which offers less resistance when the body is moving fairly slowly-the medium in this prob- lem or the one in Problem 2? Does your answer seem consistent with the observed behaviors of x(t) as t → o? Assuming resistance proportional to th
Transcribed Image Text:4. Consider a body that moves horizontally through a medium whose resistance is proportional to the square of the velocity v, so that dv/dt = -kv². Show that %3D v(t) : 1+ vokt h01 and that 1 x(t) = xo + In(1 + vokt). k Note that, in contrast with the result of Problem 2, x(t) –→ +o as t → +o. Which offers less resistance when the body is moving fairly slowly-the medium in this prob- lem or the one in Problem 2? Does your answer seem consistent with the observed behaviors of x(t) as t → o? Assuming resistance proportional to th
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