Relative velocity of third object

[Dale]

Actually celerity (also known as proper velocity) is the other way round. In the example being discussed, the celerity of the "moving" object relative to the "stationary" frame is distance measured in the "stationary" frame divided by time measured in the "moving" frame.

Celerity is larger than velocity, because time measured in the "moving" frame is shorter than time measured in the "stationary" frame. And the celerity of light is infinite. At low speeds where relativistic effects are negligible, celerity is almost identical to velocity.

Celerity = \gamma x velocity​

Although some people have described celerity as rapidity, "rapidity" usually means something else ("hyperbolic angle").

Thanks for the clarification. Having never used it I was concerned that I may have been making exactly that mistake.

 

[Dale]

So the actual velocity will be different from that observed from stationary frame and can attain a value higher than that of 'c'. You believe that this calculation is rapidity or celerity.
Could you please give me some links or references, so that i will be able to know more about this

As I mentioned before I have never used it myself because I find this kind of mixed-frame calculation very confusing. It seems that it is also confusing for you, so I would recommend against using it and I would instead recommend that you stick with single-frame and invariant measures.

My point was primarily that if you take distance in one frame and time in another frame you do not get velocity in any frame! So the fact that some number which is not velocity happens to be greater than c does not pose any problem.