T track is a great time to relax, despite your neg reps. There's nothing for you to study, but if its only gonna last for a couple weeks, then definitely get your head in the game. Power school is no joke! That is your primary goal and reason for existing at this place, keep that in mind. And for god's sakes, do NOT be associated with under-age drinking of ANY SORT. READ: "Do NOT go to house parties". YOU will take the hammer for being "of age".
That said, it can last anywhere between 2 weeks to 24 months. When I was in, most of the time you had to wait was based on 2 things: class up time, and if you had your clearance or not. Back then there were some "shady" dealings going on with the clearance guy (lack of paperwork) that kept some people on t-track for a long time. When you get on t-track, you will find out how long you will be on it for. If you already have your clearance, then expect a short stay, and don't be worrying about "bars" and "clubs" too much. Plenty of time for that later.