Nick, there is no magic formula but the slower the shutter speed with respect to the vehicle the greater the background motion blur. It very much comes down to how well you can steadily pan the vehicle and maintain focus, unless pre-focusing.
As an example the speed of this car would have been near on 150 mph and it was shot at 1/160s, 1/125 or 1/60 would have been better.
For road vehicles travelling at speeds around 50 mph start with a speed around 1/125s, practice your panning with the aim to reducing shutter speeds to a stage where you are happy with the number of keepers. I tend to play a bit on the conservative side as I want to achieve keepers for each car competing.
As for tripod use I have never attempted it, I suspect it may be possible if using long focal lengths which makes things easier.