The Addition Of Velocities In Classical Mechanics
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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.