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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" , 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 \vec{r}(t) = (4.0t^{2}-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. 4.0t^{2}-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 - 3t^{2}, 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 1^{2} h. At the end of the second second, it should be at 2^{2} h. 4-1=3, the answer is c.
1. An object moves in two dimensions according to \vec{r}(t) = (4.0t^{2}-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. 4.0t^{2}-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 - 3t^{2}, 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 1^{2} h. At the end of the second second, it should be at 2^{2} h. 4-1=3, the answer is c.
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