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Motion Question (Dynamics)

  1. Oct 21, 2007 #1
    [SOLVED] Motion Question (Dynamics)

    EDIT: I just realised this question was better suited in this forum than the engineering one, sorry :(

    1. The problem statement, all variables and given/known data

    The rocket sled starts from rest and accelerates at a = 30 + 2t until its velocity is 400m/s. It then hits a water brake and its acceleration is a = -0.003v^2 m/s^2 until its velocity decreases to 100 m/s. What total distance does it travel?

    2. Relevant equations

    v = u + at
    s = ut + at^2/2
    v^2 = u^2 + 2as

    3. The attempt at a solution

    I'm pretty sure my first part is correct but here it is anyway:

    v = u + at
    v = u + (30 + 2t)t
    *Sub in values and i get t = 8.508s, then i get s = 1701.652m from the other equation

    For the next part ive done this:

    a = -0.003v^2
    v dv/dx = -0.003v^2
    dv/v = -0.003dx *integrate both sides

    ln(v) = -0.003x + C

    when v = 400, x = 0, C = ln(400)

    ln(v) = -0.003x + ln(400)

    so when v = 100, i get x = 462.098m

    So the total distance i get is 2163.750m but the answer says 2300m....

    Where did i go wrong or is the answer given incorrect? :S
  2. jcsd
  3. Oct 21, 2007 #2


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    The equations you give only hold for constant acceleration. The acceleration function you give (a=30+2t) is not constant, and so you will need to use calculus to solve even the first part.
  4. Oct 21, 2007 #3
    Ahh whoops, i see it now :)

    Now i get the first part with t = 10s and a displacement of 1833.333m

    Thanks cristo!
  5. Oct 21, 2007 #4


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    Staff Emeritus
    Science Advisor

    You're welcome!
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