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Homework Help: Have I done this right?

  1. Mar 26, 2009 #1
    I have done M1, M2, C1 C2 C3 & C4 (A level maths modules, M meaning mechanics and C meaning core/pure). In M2 we learnt how to predict how a particle moves under gravity when projected at an angle, and we always ignored air resistance. In C4 we have learnt how to integrate a whole range of functions. This is not homework or school work

    I wondered how to predict the movement of a particle if the air resistance WAS taken into account. So I tried to figure it out and I just need to know if I have done it right. Here is the [very simple] example:

    A particle of mass one kg is initially travelling at 10m/s, air resistance is equal to a tenth of its current velocity. Find its velocity in terms of time.

    I wrote:

    F = ma
    v/10 = a
    a = v/10

    acceleration is also dv/dt so:

    dv/dt = v/10
    1/v dv = 1/10 dt
    integrate both sides you get:
    ln(v) = t/10 + lnA
    v = Ae^(t/10)

    t = 0, v = 10

    10 = Ae^0

    so final answer is:

    v = 10e^(t/10)

    is this right? is there another way to do it?
  2. jcsd
  3. Mar 26, 2009 #2


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    Staff Emeritus
    Science Advisor

    That's almost right.

    a = -v/10, meaning that acceleration is negative (deceleration), i.e. v is decreasing.

    There is an initial velocity vo = 10 m/s, at t = 0.

    Make sure the limits of integration are correct.
  4. Mar 26, 2009 #3
    Thanks, although haven't I already taken the initial velocity into account?

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