Suppose that an object is traveling along a path $A$, and let $p$ be a point on $A$. If the object’s speed along the given path is doubled, what happens to the curvature of the path at $p$?
I answered the curvature doubles but the answer is nothing. Could someone please explain?
Of course the curvature describes the path and has nothing whatsoever to do with speed. So no matter how fast the object is traveling at point $p$, the curvature at $p$ is the same.
Just think of driving along a curved highway exit. The curvature of the road (path) is literally set in concrete, and has nothing whatsoever to do with how fast someone travels along it.