I'm working on parametric equation and motion along curve right now and I get confused by the concept of slope of velocity.
My book says that (dy/dt)/(dx/dt) is the slope of velocity. And it's also the slope of the parametric curve (position curve?) I got confused by the phrase "slope of velocity". From what I've read, it doesn't seem to be the same thing as "slope of velocity curve". Can someone please explain this concept to me?
Also, if slope of velocity = slope of position = dy/dx, what's gonna be the slope of velocity curve? d^2y/d^2x? Or d^2y/dx^2?
If it is said that velocity and acceleration are perpendicular, does it mean that their slopes multiply to -1? Or the slopes of their curve multiply to -1?
Thanks in advance!