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Unformatted text preview: MATH 138 Assignment 5 Spring 2009 More differential equations. Sequences (part I). Submit all problems marked (*) and the Maple Lab question by 12:30 p.m. on Friday, June 12. 1. A Calculus book with mass m is dropped from rest and we assume that the resistence of the air is proportional to the speed of the object. If s ( t ) is the distance dropped after t seconds, then the speed is v ( t ) = s ( t ) and the acceleration is a ( t ) = v ( t ). If g is the acceleration due to gravity, the downward force on the book is mg- cv , for a positive constant c , and Newton’s Second Law gives m dv dt = mg- cv. (a) Solve the equation. (b) Find the limit of the velocity as t approaches ∞ . (c) Find the distance the book has fallen after t seconds. 2. ( * ) The Fechner-Weber law in psychology models the relationship between actual intensity and perceived intensity. It states that, at any given moment, the rate of change of perceived intensity p with respect to actual intensity a is inversely proportional to actual intensity. For example,is inversely proportional to actual intensity....
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