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Help with time/acceleration problem

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    An object starts from rest at the origin and accelerates for a time t (x axis). Acceleration is constant. Object continues with same acceleration for an additional one second. The distance traveled during time t is one half the distance traveled during the one second interal' Find the time t.


    2. Relevant equations
    These are guesses. Total time = t+1.0s.
    Total distance = x + 1/2x = 1.5x



    3. The attempt at a solution
    I haven't been able to figure this out. I keep going in circles.
     
  2. jcsd
  3. Feb 2, 2009 #2

    LowlyPion

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    Welcome to PF.

    What is the relationship between distance and time for an object under constant acceleration?
     
  4. Feb 2, 2009 #3
    I've been playing with these equations: v = 1.5x/(t+1.0s)
    a = (1.5x)/(t+1.os)2

    Am I on the right path?
     
  5. Feb 2, 2009 #4

    LowlyPion

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    I would prefer to see you rely on the relationship that x = 1/2*a*t2
     
  6. Feb 2, 2009 #5
    I think I'm doing something fundamentally wrong because I try:

    1.5x = 1/2* 1.5x/(t+1.0s)2*(t+1)2
    But then I end up with 1.5x = 0.75x, which is obviously incorrect.
    Something isn't clicking with me and this problem.
     
  7. Feb 2, 2009 #6

    LowlyPion

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    Not quite.

    You have 3/2*(1/2*a*t2) = 1/2*a*(t + 1)2

    Just solve for t. Eliminating 1/2*a directly :

    3/2 t2 = (t + 1 )2

    Take the square root of both sides ...
     
  8. Feb 2, 2009 #7
    I don't think it works. This ends up being : (the squared root of 6)/2*t = t + 1.
    The x variable I was using in 1.5x was under the assumption that distance x + 1/2x = Total X. So I don't think I can plug 1/2*a*t2 into the 1.5x, or 3/2x side of the equation. What do you think?
     
  9. Feb 3, 2009 #8

    LowlyPion

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    The 1/2 a*t2 is already the distance you call x.

    The 3/2*x then is 3/2*(1/2*a*t2) and from the statement of the problem that's the same as !/2*a*(t + 1)2

    As to the answer you got, I'd recheck your math.
     
  10. Feb 3, 2009 #9
    I appreciate your help but I'm still confused. I'll keep pluggin away at it. I tried a different setup for time. I tried Total time = t, one portion of t (for distance x) would be 1.0s and the other distance (1/2*x)would be t-1.0s. I'm just not sure how to solve for t with the information supplied in the problem. I know the answer is 1.37s but I can't figure out how to arrive at that.
     
    Last edited: Feb 3, 2009
  11. Feb 3, 2009 #10

    LowlyPion

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    I think I see the problem. I made the same mistake.

    The statement of the problem says that

    xt = 1/2*(xt+1 - xt)

    This means that

    3xt = xt+1

    not 3/2.
     
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