[amluto]

Careful!

> What happens with a ball (or with a thrown stone) will differ depending on whether its velocity is positive or negative, and so on.

The velocity of a ball is a vector. Using a positive or negative number to describe it is a manner of convention. When you say that you threw a ball with “positive 7 mph” velocity, you need to explain what you mean.

One might argue that there really is a ball and that it has a velocity and that the velocity really is an element in a vector field originating [0] at the center of mass of the ball. Debating to what extent this is fundamentally true or is just a useful concept that people came up with would be interesting.

[0] In general relativity, space is not Euclidean (nor is it a flat Minkowski space), and velocity vectors are only really meaningful in association with a point in spacetime. You can read all about tangent bundles in Wikipedia :)