# 2007 F=ma Contest

1. Jan 27, 2009

### myanmar

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 $$\vec{r}$$(t) = (4.0$$t^{2}$$-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. 4.0$$t^{2}$$-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 - 3$$t^{2}$$, 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.

Last edited: Jan 27, 2009
2. Jan 27, 2009

### LowlyPion

That looks ok.

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

(4 - 5)/ 1 = -1

3. Jan 27, 2009

### praharmitra

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.