Results 1 to 3 of 3

Math Help - Particle moving on a line.

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    54

    Vector calculus on particle movement

    Hello,
    I'm currently working on a question which is about a particle moving across along a line. The particle is moving along the line log (x) at a constant speed of one. When t = 0, the particle is at point (1,0). I have to find a) the velocity vector and b) the acceleration vector at (1,0).
    I've start off by making r(t) = (x(t), \log (x(t)). To find the velocity vector, I must differentiate r(t). So: v(t) = r'(t) = (x'(t), \frac{x'(t)}{x(t)}). This is where I get stuck. I know that the speed of the particle is 1 at any time t. So \mid v(t)\mid = x'(t)\sqrt{1+\frac{1}{(x(t))^2}}=1. I feel I need to find the value x'(t). Is this right? If so, how do I find it?
    Thanks for your help.
    Last edited by Silverflow; February 16th 2010 at 05:08 PM. Reason: Mistakes in question
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    69
    This looks to be a differential equations problem. You've got \frac{dx}{dt} \sqrt{1 + 1/x^2} = 1 and you want to find x. This is a separable equation which can be solved by taking  \sqrt{1+1/x^2} dx = dt and integrating both sides. The fact that when t = 0, x = 1 gives you an initial condition. The problem is that integral on the left hand side is pretty nasty. I'm not sure that you'll be able to solve for x after all is said and done. Maybe see if someone on the differential equations board can figure this out.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    54
    Thanks, mate. I'll do just that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Particle moving
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 8th 2010, 01:51 PM
  2. Replies: 1
    Last Post: May 13th 2009, 09:32 AM
  3. moving particle
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 16th 2008, 07:25 PM
  4. moving particle
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 27th 2007, 10:27 PM
  5. moving particle with friction
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: February 5th 2007, 02:43 AM

Search Tags


/mathhelpforum @mathhelpforum