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2007 F=ma Contest

  1. Jan 27, 2009 #1
    I'm going through the 2007 Physics Olympiad F=ma test tonight (first 27 questions). It's available here, if you're wondering. I'll post my attempts here as I get to them. Tell me what I'm doing right or wrong. I don't really know this stuff, I'm taking AP Phys. C Mechanics right now.


    1. An object moves in two dimensions according to [tex]\vec{r}[/tex](t) = (4.0[tex]t^{2}[/tex]-9.0)î + (2.0t-5.0)ĵ. where r is in meters and t in seconds. When does the object cross the x-axis?
    (a) 0.0 s (b) 0.4 s (c) 0.6 s (d) 1.5 s (e) 2.5 s
    From what I have picked up, i and j represent x and y in the coordinate plane (and k is z). I would think that it would cross the x axis when the stuff next to the y becomes zero. 4.0[tex]t^{2}[/tex]-9=0 when t=1.5. So, my answer is d.

    3. The coordinate of an object is given as a function of time by x = 8t - 3[tex]t^{2}[/tex], where x is in meters and t is in seconds. Its average velocity over the interval from t = 1 to t = 2s is
    (a) -2 m/s (b) -1 m/s (c) -0.5 m/s (d) 0.5 m/s (e) 1 m/s
    Well, velocity is just the derivative of position, so it would be given by v=8-6t. Since that's linear, the average of that is at the point t=1.5s, which means the answer is -1 m/s, b.

    4. An object is released from rest and falls a distance h during the first second of time. How far will it fall during the next second of time?
    (a) h (b) 2h (c) 3h (d) 4h (e) h^2
    Acceleration is 9.8 m/s^s down, and position is the double integral of that which means it's quadratic. So, in the first second it should have fallen [tex]1^{2}[/tex] h. At the end of the second second, it should be at [tex]2^{2}[/tex] h. 4-1=3, the answer is c.
     
    Last edited: Jan 27, 2009
  2. jcsd
  3. Jan 27, 2009 #2

    LowlyPion

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    That looks ok.

    I would treat the #3 differently. V = Δx/Δt

    (4 - 5)/ 1 = -1
     
  4. Jan 27, 2009 #3
    1. You are right. But the "stuff' next to y is 2t-5 and not 4t^2 - 9. You found out when it'll cross the y-axis.

    4. This particular answer is right. But i dont think this analogy would work if the body was not thrown from rest. In that case the answer would depend on the initial velocity.
     
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