Hello!
I'm having the exact same problem on most courses. Most of the times it happens about five seconds after the start of the race and sometimes after 30 seconds or one minute. I'm using Windows Vista.
These are known issues. Faster computers will handle more opponents better but slower ones have big problems. The code is not efficient enough to have many cars on track at a time yet. A fix for this will hopefully come in the upcoming release (whenever that is) or if we release early and it doesn't make it, the next one.