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musicfairy
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Homework Statement
This is from the 1983 ap test. I'm using it to study the concepts but so far it only confused me more.
It goes:
A particle moves so that the x-component of its velocity has the constant value vx = C; that is, x = Ct
1. Determine the y-component of the particle's velocity as a function of x.
2. Determine the y-cpmponent of the particle's acceleration.
Part b.
Suppose, instead, that the particle moves along the same parabola with a velocity whose x-component is given by vx = C/(a+x2)1/2
3. Show that the particle's speed is constant in this case.
The Attempt at a Solution
I have the solution, but it doesn't make any sense to me. For the first question they showed dy/dt = (dy/dx)(dx/dt) They said it's the chain rule, but where did that come from? I thought I knew the chain rule until I saw that. Where did t come from?
I can't figure out where the answer to the 2nd question is from either. They put ay = (dvx/dt) = (d/dt)(C2t) = C2
I can't figure out where that came from either.
Number 3 confuses me even more than the previous 2. This is what they did:
v = sqrt(vx2 + vy2)
vy = dx/dt = (dy/dx)(dx/dt) = xvx
v = sqrt((vx2)(1 + x2)) = sqrt( (C2/ 1+x2)(1 + x2)) = C
If you have access to 1983 mech #1 everything looks much better than what I typed.
Can someone please explain all this to me? I'm trying to prepare for the ap test by looking at old problems, but so this one is written in hieroglyphics and I could really use some help.
And please explain how the chain rule makes dy/dx = (dy/dx)(dx/dt)
Any help is greatly appreciated.
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