I'm trying to figure out how fast a switch or
relay acts when it is activated or "switched". I'm not so worried about the time from when the relay is triggered to when the switching is done, but the time from when the relay moves from one throw to another (I'm interested the same for a switch) - so I'm trying to find out the amount of time for the transition between the two throws.

I need to switch something very quickly from one power source to another and I need to find out what I need to do this. I estimate I have about 1/20th of a second to make the switch (so about .05 seconds). I need to switch 3 wires so a (3P2T) and handle 7A 120v. I couldn't find speed ratings on mechanical switches so I have no idea what range they fall in and they would be much better to work with in my case.

 

Is it possible to use a SS approach such as a SSR's.?
As a rule the physically larger the mechanical relay the slower the action of the armature.
Max.

 

I'm trying to figure out how fast a switch or
relay acts when it is activated or "switched".

That would be covered in the Relay or Switch data sheet. For example I have an outdated Omeron Relay sitting here on my desk. Part Number: MK3P5-S and if I look up the data sheet I find this data sheet which contains this data in part:

Contact resistance 50 mΩ max.
Operate time AC: 20 ms max. DC: 30 ms max.
Release time 20 ms max.

Incidentally you do not mention if the load is resistive or inductive and is the 120 V 7 A AC or DC? The relay I linked to has a 3PDT version and it looks like it would work for what you want. Another possibility, as Max mentioned, is the use of solid state switching.

Ron