1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kinmatic question involving differential equation

  1. Apr 28, 2010 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m falls fom rest; the resistance of the air when the speed is v is kv2 where k is a constant. If s is the distance fallen in time t, prove that s = V2/2g ln(V2/(V2-v2)), where V2=mg/k

    2. Relevant equations

    3. The attempt at a solution
    I have already proven that t = V/2g ln((V+v)/(V-v)). How do I make use of that equation to solve the problem? Do I have to change to v(t) equation and integrate it?
  2. jcsd
  3. Apr 28, 2010 #2


    User Avatar
    Homework Helper

    Yes, this is one way. Integrating v(t) you get s(t), but you need the s(v) relation, so you have to substitute t(v) for t.

    The other way is that you transform the original differential equation:

    dv/dt= g-k/m * v^2

    by considering s the independent variable and applying the chain rule during differentiation with respect to t.

    dv/dt=dv/ds*ds/dt = dv/ds *v .

    The new differential equation is : v dv/ds = g-k/m*v^2.
    This is separable, easy to solve with the condition that v=0 at s=0.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Kinmatic question involving Date
Kinematics Mechanics Oct 8, 2016
A Couple more "Rotation of Rigid Bodies" questions Nov 8, 2015
Sketching Kinmatic Graphs Feb 20, 2012
Simple kinmatics Feb 16, 2005
Kinmatics problem Sep 28, 2004