View source for PlanetPhysics/Theorem of the Addition of Velocities Employed In

\subsection{The Theorem of the Addition of Velocities Employed in
Classical Mechanics}
From [[../SpecialTheoryOfRelativity/|Relativity: The Special and General Theory]] by [[../AlbertEinstein/|Albert Einstein]]

Let us suppose our old friend the railway carriage to be travelling
along the rails with a constant [[../Velocity/|velocity]] <math>v</math>, and that a man traverses
the length of the carriage in the direction of travel with a velocity
<math>w</math>. How quickly or, in other words, with what velocity <math>W</math> does the man
advance relative to the embankment during the process? The only
possible answer seems to result from the following consideration: If
the man were to stand still for a second, he would advance relative to
the embankment through a distance <math>v</math> equal numerically to the velocity
of the carriage. As a consequence of his walking, however, he
traverses an additional distance <math>w</math> relative to the carriage, and hence
also relative to the embankment, in this second, the distance w being
numerically equal to the velocity with which he is walking. Thus in
total be covers the distance <math>W=v+w</math> relative to the embankment in the
second considered. We shall see later that this result, which
expresses the theorem of the addition of velocities employed in
[[../NewtonianMechanics/|classical mechanics]], cannot be maintained; in other words, the law
that we have just written down does not hold in reality. For the time
being, however, we shall assume its correctness.

===References===
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. [http://www.marxists.org/reference/archive/einstein/index.htm Einstein Reference Archive] which is under the FDL copyright.

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