# The Relativistic Train

Really cool post I found on one of my favorite physicist’s blog.  It’s just a derivation for the relativistic addition of two velocities.

Typically you would think that to add two velocities you just add them together.  Ex. if someone is walking at a velocity $u$ on top of a train moving at velocity $v$, then to find out the velocity the person is moving relative to the ground you would normally just add the velocity of the train and the velocity of the person walking. $w = u+v$.

This gives a fairly accurate answer in most cases, but when you start approaching the speed of light this isn’t the case according to Einstein’s theory of relativity.  Instead the real equation for adding velocities looks like this:

$w = \frac{(u+v)}{1+\frac{uv}{c^2}}$

Take a look at the reason why