Relative Velocity of Particle ##p##: S vs S

[Apashanka]

TL;DR

Considering two frames S(absolute rest) and S' where S' is moving with respect to S with a velocity $c\hat i$

A particle $p$ is moving with a velocity $u\hat i$ with respect to S ...
The velocity of $p$ with respect to S' is then $-c \hat i$...

Another part...
Similarly taking the velocity of particle $p$ with respect to S' as $-c\hat i$ the velocity of $p$ with respect to S is then coming to be undefined ,however it should be coming to be $u\hat i$??isn't it...

 

[Dale]

Unfortunately there is nothing we can discuss here. The idea of absolute rest is non-physical and even in theory there is no such thing as an inertial frame moving at c with respect to another inertial frame.