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 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. 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 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.