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!
I'm still a little confused on some points. When you say "the product of the slopes would be -1 ", do you mean velocity's derivative and acceleration's derivative, since you said "Slope of velocity" implies acceleration"?
Regarding the slope of velocity, I had the same idea as you but my book seems to have a different say. Here's how it explains it (rephrased):
Let's say v = (3,5) = 3i + 5j
Graph on a paper 3 units right and 5 units up. The slope = Δy/Δx = 5/3.
So dy/dx = slope of velocity as well as slope of the curve