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A mass m is accelerated by a time-varying force exp(-ßt )v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv m dt exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.

A mass m is accelerated by a time-varying force exp(-ßt )v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv m dt exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.8: Joint And Combined Variation
Problem 7P
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A mass m is accelerated by a time-varying force exp(-ßt )v², where v It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore its velocity. dv m dt exp(-ßt)o³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.
Transcribed Image Text:A mass m is accelerated by a time-varying force exp(-ßt )v², where v It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore its velocity. dv m dt exp(-ßt)o³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.
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