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**Galilean or Classical relativity equation**

v_{AE} => Velocity of A with respect to Fixed Frame

v_{BE} => Velocity of B with respect to Fixed Frame

v_{AB} => velocity of A with respect to B

v_{AB}=v_{AE} – v_{BE}

or

v_{AB}=v_{AE} + v_{EB}

Let

v_{AE} =10 m/s( towards positive x-axis)

v_{BE} =6 m/s ( towards positive x-axis)

v_{AB}=10-6 =4 m/s

This equation works well for normal velocities but it does not hold good for speed reaching speed of light

**Relativistic Velocities**

Suppose

v_{AE}= 0.6c

v_{EB}= 0.8 c

Using the classical relativity equation above, you get

v_{AB}=v_{AE} + v_{EB} = 0.8c + 0.8c = 1.6c

In other words, this predicts that A will measure B’s velocity as 1.6 times the speed of light, which is forbidden by Einstein’s Special Theory of Relativity, which says, among other things, that the speed of light is the ultimate speed limit in the Universe.

In Special Relativity the classical equation is modified to be:

$v_{AB}=\frac{v_{AE}+v_{EB}}{1+\frac{v_{AE}v_{EB}}{c^{2}}}$

So Using Special Relativity, we get:

v_{AB}=.98 c

In other words, A would measure B’s velocity as 98% of the speed of light.