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Math Help - Forming a DE from F=ma

  1. #1
    Super Member craig's Avatar
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    Forming a DE from F=ma

    A particle of mass m is projected with speed u along a straight horizontal track. The first section of the track has length d. On this section of the track the motion is resisted by a
    constant force of magnitude mk, where k is a positive constant. The particle does not come to rest on this first section of the track.

    Show that the speed V of the particle at the end of the first section of the track is given by:

    V = \sqrt{u^2 - 2kd}

    Using the equation ma = F, I got the following equation.

    If we let the speed of the particle = v

    m\frac{dv}{dt} = v-mk, however in the solutions they just have m\frac{dv}{dt} = -mk, what's happened to the v, I would have thought that the forces acting on the paticle would be v and -mk?

    Thanks for the help
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  2. #2
    Senior Member roninpro's Avatar
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    If you think about your units for a second, v cannot possibly be a force.
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  3. #3
    Super Member craig's Avatar
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    Ohh yeh, actually that's rather obvious isn't it :S Think I must be used to dealing with a constant force produced by the engine.

    Thanks for spotting that obvious mistake!
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