Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving problems in Kinematics with simple calculus

  1. May 12, 2013 #1
    Hi,

    I have a generic question about solving kinematic problems using simple calculus. For eg.
    A variable force F = bv (v is instantaneous speed at some time t) acts on a vehicle moving with speed v. Suppose the initial speed at t = 0 of the vehicle is v0. Calculate the distance through which it moves before stopping.
    By work energy theorem, (1/2) m (V0)2 = ∫ F. ds
    Now how do we integrate the right side and move forward? That's my main question. Any help is appreciated

    Thanks
    Sanjay
     
  2. jcsd
  3. May 12, 2013 #2
    b above is a constant.
     
  4. May 12, 2013 #3

    Philip Wood

    User Avatar
    Gold Member

    I wouldn't start from here. I think (though I may be wrong) that the theorem in this form is not much use when the force is velocity-dependent.

    Instead, assuming that the vehicle is confined to move in a straight line, you can use Newton's second law in the form F= ma. Substitute bv for F (remembering that b is negative - I'd write it as -β] and substitute dv/dt for a. This gives you a differential equation, which is easily solved to give v as a function of t. Integrate this wrt time, between zero and infinity to give you the distance gone.

    This is quite interesting, as it shows that the vehicle goes a finite distance, but takes an infinite time to do it! (Well, to do every last nanometre). This is not what a real vehicle would do, because F = -βv does not model the usual rolling resistance, bearing friction etc. very well. These will not tend to zero as the vehicle's speed goes to zero.
     
    Last edited: May 12, 2013
  5. May 12, 2013 #4
    A note on terminology. Any problem involving forces is dynamical, not kinematic.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving problems in Kinematics with simple calculus
Loading...