Addition Of Velocities Employed In Classical Mechanics

The train is travelling with a constant velocity v. A man walks from the back of the train movig forward in the direction of travel with a velocity w.

How quickly, or with what velocity W, does the man advance relative to the embankment?

If the man were to stand still for a second, he would advance relative to the embankment through a distance v equal numerically to the train’s velocity.

As a consequence of his walking, however, he travels an additional distance w relative to the train. Hence, he is also relative to the embankment. In this second, the distance w is numerically equal to his walking velocity.

Thus, in total he covers the distance W = v + w relative to the embankment in that second.

This result shows the theorem of the addition of velocities in classical mechanics. But this theorem does not hold in reality.

For the time being, however, we shall assume its correctness.