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e velocity v of a mass m in fall subject to an air resistance proportional to the instantaneous speed is

e velocity v of a mass m in fall subject to an air resistance proportional to the instantaneous speed is

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter1: Getting Started
Section: Chapter Questions
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A differential equation describing the velocity v of a mass m in fall subject to an air resistance proportional to the instantaneous speed is

m dv/dt=mg-kv,

where k is a positive proportionality constant.

a) Solve the equation, subject to the initial condition v(0) = v0

b) Calculate the limiting speed of the mass.

c) If the distance s is related to the speed by ds/dt = v, derive an equation
explicit for s, if it is also known that s(0) = s0

topic:ORDINARY DIFFERENTIAL EQUATIONS

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