See our user-submitted Swoop Racing Strategies for tips. After the second heat and your new record, the mechanic will announce that no one can beat your time and you'll win the Swoop Race, collecting 330xp. For the first heat, the best time will be incredibly easy to beat and once you do you'll find that another racer has bested your score, so attempt to make it on the slower side if you're very good.
You'll have two heats to race in, and you can even practice before hand. This is the one to talk to for beginning the race. After you're finished with the mechanic, you can talk with the other swoopies at the race or simply see the race organizer at area #2. Don't let it bother you - it won't break down. He'll give you the lowdown on the rules, and try and instill a bit of fear in you due to the 'instability' of your new swoop accelerator.
You'll talk to this mechanic in the morning of the Swoop Race and receive the 630xp (or both the xp and 500 credits, depending on who you sided with) for getting this far.