I think the 70-200 is too short. Get a 300, like a 300 f/4 or something used. I've also seen great racing shots with the Bigma 50-500. I presume your shooting daylight, this lens should be all you need!
Shutter speed depends on the speed of the cars. (Don't you just love non-answers). Slower the cars => slower the shutter => better the motion blur. Essentially, try and get as slow as you can while keeping the car nice and sharp.
I don't have any experience shooting cars in the evenings. What sort of car racing is it? Short track/quarter mile ovals/sprint cars or longer tracks?
If it's short track stuff then your 70-200 may be enough, although 300mm f/2.8 would be ideal (not that I have one, but one day, one dayyy). The 300 would be great for just about any motorsport.
VR, by the way, is great for panning! The 70-200 has a setting you need to attend to that makes the lens allow swept side to side motion, while stabilizing up and down motion, so you can pan for a lot longer than without VR. I don't have the same lens you do, but at 120mm I can pan for a good fraction of a second and keep the subject still with the 'baby VR'. This one's at a tenth:
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