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Help on this problem :S

  1. Jun 16, 2004 #1
    Here's the question

    The equation of motion of a particle moving in a straight line is:

    [tex]s = kv^2ln v[/tex]

    where k is a constant and v is the velocity. Find an equation that expresses the acceleration in terms of velocity.

    I need some help on this problem. I'd post my work but I don't exactly have time, and I need to know how to do this by tomorrow morning.

    The answer is [tex]a = \frac {1}{k(1+2ln v)}[/tex]

    Thanks in advance, Warr
  2. jcsd
  3. Jun 16, 2004 #2
    Apply the Chain Rule

    Let [itex]u = v^2\ln{v}[/itex] and then use the chain rule (and remember that [itex]v = ds/dt[/itex] and [itex]a = dv/dt[/itex]).
  4. Jun 16, 2004 #3
    Differentiate both sides of the equation with respect to t.

    Note that the left hand side will turn into velocity, and the right hand side will turn into some function of v and dv/dt (i.e. acceleration).

    Now solve for a.

  5. Jun 16, 2004 #4
    Thanks guys, I completely forgot that dv/dt was a!
  6. Jun 16, 2004 #5


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    There's another neat way to do this.

    Notice that a=dv/dt=(dv/dx)(dx/dt)=v(dv/dx)

    Since you have x=f(v), find dx/dv and invert it to get dv/dx. Multiply this by v and you have your answer !
  7. Jun 16, 2004 #6
    So when v = 0...?
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