The Addition Of Velocities 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.