It can be hard to say, exactly, as there are a lot of factors outside of just the rider category. Not all velodromes are equal - some are "faster" than others. The quality of the surface, the degree of the banking, the length of the track, whether it's indoors or outdoors, elevation, etc. all effect the speed of the riders.
At my local velodrome (Kissena) the averages seem to be 13-16 seconds for Cats 4/5, and 12-14 seconds for Cats 1/2/3. The fastest time recorded in the last 8 years or so (at least, in the records I checked) was 11.91 seconds.
The world record is held by Theo Boss at the Moscow velodrome (often considered the fast velodrome for the 200m) at 9.77 seconds.