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How far does the car travel? Uniform acceleration.

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data

    A car accelerates uniformly from rest to a speed of 23.2 km/h in 5.4s. Find the distance it travels during this time. Answer in units of m.

    2. Relevant equations

    [itex]\Delta[/itex]x = 1/2(vi + vf)t

    vf = vi + at

    vf2 = vi2 + 1/2 at2

    3. The attempt at a solution

    I have used each one of these equations, sometimes in combination, and every time I reach the answer 1044m, which is wrong. I think the problem lies not in which equations I use, but in the way I set them up. Here's one way:

    23.2km/hr = 23,200/60 = 386.7 m/s
    [itex]\Delta[/itex]x = 1/2(vi + vf)t
    [itex]\Delta[/itex]x = 1/2(0 + 386.7)(5.4)

    I'm really stuck on this one and would really really really appreciate some help. I don't see what I'm doing wrong, because I've always arrived at the same answer (1044m) no matter which way I solve for it. This makes me think I'm using the wrong initial velocity or something like that.

    Thank you so much!

    Edit: I have also solved for acceleration and plugged it in. I got 71.6 m/s2. After using acceleration in one of the equations, I still got 1044m.
     
    Last edited: Sep 27, 2011
  2. jcsd
  3. Sep 27, 2011 #2
    I haven't gone through the whole problem but I see at least one part that is not correct.

    "...23.2km/hr = 23,200/60 = 386.7 m/s..."

    Look at your conversion factor going from hours to seconds.
     
  4. Sep 27, 2011 #3
    Thank you very much :smile:

    Do you know if this problem requires that I find acceleration?
     
  5. Sep 27, 2011 #4
    You are very welcome.
     
  6. Sep 27, 2011 #5
    No, it would not. But convince yourself of that. Take one of the equations that uses velocity only to find the displacement, and use one that uses the acceleration and compare the answer you get.
     
  7. Sep 27, 2011 #6
    The answer was 17.28m. Thank you all for being so helpful!

    Unfortunately, that was one of the easiest problems I have to do, and I didn't get that one because of a conversion mistake.

    Time to hurt my brain on a problem with systems of equations and quadratic stuff (It sucks being in honors physics while just starting to take algebra II).
     
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