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Homework Help: Can someone check my work?

  1. Dec 4, 2005 #1


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    Ive got 2 questions that I would like looked at.

    Question 1:
    A rocket sled has the following equation of motion: 6vdot = 2700 - 24*v. How long must the rock fire before the sled travels 2000 m? The sled starts from rest.

    I took the integral which of that equation which gamve me v(t) = 2700*t - 24*x. At rest v = 0. So 0 = 2700t - 24*(2000)

    Solve for t and you get t = 17.78 seconds.

    Does this look right? If not please let me know.

    Question 2:
    For each of the following models, obtain the free response and time constants if any.

    16*xdot + 14*x = 0, x(0) = 6

    I changed it to v's, which gave me 16*v + 14*vdot = 0, v(0) = 6

    For time constant its c/m so tau = 14/16 = .875

    Then for the free response its v(t) = v(0)*e^-t/tau

    So for my final answer, v(t) = 6*e^-1.143*t

    If there are any problems with this, can you please let me know where.

    I just want to make sure Im doing this right.
  2. jcsd
  3. Dec 4, 2005 #2


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    Gold Member

    The question says that the sled starts from rest, not that it is at rest after it has traveled 2000m.
  4. Dec 4, 2005 #3


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    So I should have a variable still I guess for my v(t) instead of setting it to equal 0. Can you give me an idea of what it might equal?
  5. Dec 4, 2005 #4


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    I would go with another approach entirely: Solve the differential equation for v, then integrate to get an expression for x(t) with no v terms.
  6. Dec 4, 2005 #5


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    I did it a different way for Problem 1.

    I made the equation into 6*vdot + 24*v = 2700.

    Then I solved for V(t) which is the free response and force response.

    Since v(0) = 0, the free response goes away.

    leaving v(t) = F/c(1-e^(-ct/m) = 2700/4*(1-e^-4t)

    I then took the integral of that to get x(t).

    This game me x(t) = (225*e^-4t*(4t*e^(4t)+1))/8

    I then set x(t) = 2000. Solving for t I come up with 17.78 seconds which is what I originaly came up with the first time.

    Was I just right the first time? Is this coincidental or did I do it wrong this time?
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