Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that du/dt = -kv. (a) Show that its velocity and position at time t are given by v(1) = voe¬kt and x(1) = xo + () (1-e-kt). (b) Conclude that the body travels only a finite distance, and find that distance.

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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Suppose that a body moves through a resisting medium
with resistance proportional to its velocity v, so that
du/dt = -kv. (a) Show that its velocity and position
at time t are given by
v(1) = voe¬kt
and
x(1) = xo + () (1-e-kt).
(b) Conclude that the body travels only a finite distance,
and find that distance.
Transcribed Image Text:Suppose that a body moves through a resisting medium with resistance proportional to its velocity v, so that du/dt = -kv. (a) Show that its velocity and position at time t are given by v(1) = voe¬kt and x(1) = xo + () (1-e-kt). (b) Conclude that the body travels only a finite distance, and find that distance.
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