Hi john_smith,
TCAS will only demand either a 1500fpm or 2500fpm ROC or ROD.
See page 13:
http://www.skybrary.aero/bookshelf/books/106.pdf
"2000 ft/min.
1000 ft/min.
500 ft/min.
0 ft/min.
RA requires one of
these vertical speeds"
All of my TCAS warnings have been due to other traffic with big ROD / ROC approaching their cleared levels. If only they observed ICAO Recommendation:
"Unless otherwise specified in an air traffic control instruction, to avoid unnecessary airborne collision avoidance system (ACAS II) resolution advisories in aircraft at or approaching adjacent altitudes or flight levels, operators should specify procedures by which an aeroplane climbing or descending to an assigned altitude or flight level, especially with an autopilot engaged, may do so at a rate less than 8 m/sec or 1 500 ft/min (depending on the instrumentation available) throughout the last 300 m (1 000 ft) of climb or descent to the assigned level when the pilot is made aware of another aircraft at or approaching an adjacent altitude or flight level."
See
http://www.skybrary.aero/bookshelf/books/1804.pdf
So with say 3,000 ft per min ROC, pilots will have to have started to change their VS towards 1500 ft per min before 2,000 feet to go - else it is too late and the AP mode will have changed to ALT*.