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Mechanics question with variable force

  1. Dec 22, 2006 #1
    Question copied word for word

    1. A particle of mass m moves in a straight line under the action of force F where F = ms, s being the displacement of the particle from O, a fixed point on the line.
    When s = -a the velocity of the particle is u. Find the velocity of the particle when s = 0.

    2. F = ma or F= -ma (i think...)

    a = v(dv/ds)

    3. If ms = -ma, then s is always equal to -a, so the velocity would always be u, which doesnt look right... Or if I intergate:

    s = -a

    s = -v(dv/ds)

    s^2 = -(v^2) + c

    replace s with a and v with u.

    a^2 + u^2 = c

    s^2 + v^2 = a^2 + u^2

    when s = 0, a = 0

    v = u

    Where have i gone wrong?
  2. jcsd
  3. Dec 22, 2006 #2
    F = ms? Force = MassxLength? :confused:

    I think something is amiss.
  4. Dec 22, 2006 #3


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    Homework Helper

    Doesn't have to be a miss, the given force is a function of the displacement.
  5. Dec 22, 2006 #4
    Okay, fine. I suppose the constant in some set of units take the value of 1. Sorry about that.
  6. Dec 22, 2006 #5


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    Staff Emeritus
    Science Advisor

    F= ma. Don't guess- look it up.

    Why would the velocity always be u? If s is not 0 then -a is not 0: with non-zero acceleration, the velocity changes.

    You aren't really saying anything here. What is v if not u?

    You are correct that [itex]v^2+ s^2= C[/itex], a constant.

    Is "a" here some given constant? In that case, you have [itex]C= u^2+ a^2[/itex] and so the general formula is [itex]v^2+ s^2= u^2+ a^2[/itex] where u and a are given constants. When s= 0, [itex]v^2= u^2+ a^2[/itex] and so [itex]v= \pm \sqrt{u^2+ a^2}[/itex].
  7. Dec 22, 2006 #6
    If F = ma then the particle would speed off in one direction, unless it ended up or started at O with a velocity of zero. If F = -ma then you would get harmonic motion... I thought it might be plus or minus because in the question it didnt say whether the force was towards or away from O.

    I was thinking that a was acceleration, which was why i got confused... The velocity can't always be u. In the other questions the teacher used k for any generic constant and used the word acceleration instead of a symbol. I'll just guess that he meant to write k and made a mistake.
    Last edited: Dec 22, 2006
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