1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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 http://www.aapt.org/Contests/upload/olympiad_2007_fnet_ma.pdf" [Broken], 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 by a moderator: May 3, 2017
  2. jcsd
  3. Jan 27, 2009 #2


    User Avatar
    Homework Helper

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: 2007 F=ma Contest