What is the best way to specify duration of a clip? I know there is a playback rate option, but what if I wanted the duration of a track to be exact, up to a fraction of a second?
Trim the clip to that length? Is that what you're after?
If not, since you mention the playback rate i assume you want to have the entire clip play, but adjust the speed to something specific. What i would do is place the cursor where you want the clip to end, then Ctrl-Drag the right edge of the clip to the cursor (it will "snap" when you get there). This will speed it up or slow it down as necessary to exactly fill that time. You can change the speed from 0.25x to 4x with this method and the audio changes speed with it as well.