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Simple kinematics question

  1. Sep 10, 2009 #1
    1. The problem statement, all variables and given/known data
    I should know this, but it's been awhile since I've dealt w/ kinematics.

    As the simplest example of resisted motion of a particle, find the velocity of horizontal motion in a medium in which the retarding force is proportional to velocity.

    So Fr is something like -kmv, where k is a constant.

    I'm tempted to use v=vo+at in this manner:

    ma=-kmv, so a = -kv
    then v=vo-kvt
    v(1+kt)=vo
    v=vo/(1+kt)

    But my book uses integrals:
    mdv/dt=-kmv
    int(dv/v)=-k*int(dt)
    lnv=-kt+C , v= c1e^-kt where (c1=e^C) and applying initial conditions you get
    v=vo*e^-kt
    and this makes a lot of sense to me.

    So could somebody please refresh me on why I cannot solve for a and substitute into v=vo+at? I'm thinking it has to do with the constantly changing force, but I'm looking for a good explanation.
     
  2. jcsd
  3. Sep 10, 2009 #2

    rl.bhat

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    Homework Helper

    Kinematic equation v = vo + at is applicable to a motion having constant acceleration. But in the given problem acceleration is not constant.
     
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