**RELATIVISTIC ADDITION OF VELOCITIES - ADDITION OF VELOCITIES - ADDITION OF VELOCITY IN RELATIVITY**

Consider a frame
of reference s’ moving with uniform velocity v relative to a stationary frame s
along the positive x direction. A particle is moving along the positive
direction of x axis with a velocity given by dx/dt as observed by an observer
in frame s.

As observed by an observer in frame s’, he
distance travelled in dx’ in time dt’- the velocity of the particle as seen by
the observer in observer s’ is given byTo find a transformation between u’ and u we use Lorentz-Transformation which are as follows:

Differentiating Eq. (2)
and (3) w.r.t

**t’**, we obtain
Rearranging Eq. (4) and
using Eq. (8)

Equation (9) represents
the relativistic addition formula. The inverse relation will be given by

Consider two photons
approaching each other such that the velocity of each photon as observed by a
stationary observer is c. In order to calculate the relative velocity of one
photon w.r.t another

Thus
for photon B the relative speed of photon A is equal to "c".

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