On Velocity Addition (3)

Using the aforementioned definitions and assumptions, let’s solve a few more problems:

  1. If one child is chasing another, to catch up, it will take time t=d/(v1-v2).
  2. If a person is swimming across the river at speed v1, while the water is running at speed v2, then the combined speed is the vector addition result of v1 and v2.

What is the meaning of v1+v2, v1-v2, and vector addition of v1 and v2?

Relative Velocity or Relative Speed.

Actually, we have only one velocity addition rule, that is the vector addition rule of v1 and v2, as v1+v2 and v1-v2 are only special cases of it.
This should not come out as a surprise. As in all situations, we all based our work on the same set of definitions and assumptions.
So, this unqiue rule applies everywhere, whether on straight lines or curved lines, whether in inertial frames or non-inertial frames.

And we all know, the aforementioned definitions and assumptions have a formal name: Newtonian space and time.
To honor Galileo’s contribution(He pointed out that all motions are relative and nothing is at absolute rest), the velocity addition rule under Newtonian system is named after him.
In Newtonian system, all velocity additions are Galilean transformations, as there is only one velocity addition rule.