(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 v_{x}= 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+x^{2})^{1/2}

3. Show that the particle's speed is constant in this case.

3. 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 a_{y}= (dv_{x}/dt) = (d/dt)(C^{2}t) = C^{2}

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(v_{x}^{2}+ v_{y}^{2})

v_{y}= dx/dt = (dy/dx)(dx/dt) = xv_{x}

v = sqrt((v_{x}^{2})(1 + x^{2})) = sqrt( (C^{2}/ 1+x^{2})(1 + x^{2})) = 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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# Kinematics particle velocity problem

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