The pan shot is tried and true. It's been around longer than sin, and while difficult to master it is relatively easy to get usable results from.
There is really only one thing you need to worry about for the pan shot, and that's shutter speed. The proper shutter speed to use is going to depend on your ability and the speed of the vehicles. Generally speaking the range will be from about 1/250th to 1/60th. The worse your technique, the faster the shutter. The faster the cars, the faster the shutter.
So if you are right at the tree you might start with a shutter speed of 1/80th to 1/125th. If you are a ways down the track then look at 1/180th to 1/250th. Slower shutter speeds are great, but beyond a certain point they won't improve the image much, if at all. Once the background is blurred it's blurred (same with wheel spin), and you are just increasing the likelihood of blurring your main subject
So, stop down your lens until you can get a shutter speed that works. If need be don't be afraid to throw an ND filter on the front of your lens too (you don't need to worry about auto-focus degradation). If you have a lens with Vibration Reduction (optical image stabilisation) and it has a user selectable pan mode be sure to set that (for Nikon Lenses this means "VR Normal" and not "VR Active". VR Active will attempt to stabilize your panning motion which you definitely don't want)
Next up, practice without taking a picture. With an SLR the viewfinder will black out while the image is being recorded, and your ability to capture a photo is going to be limited by your ability track the car during this time. This can be quite challenging with drag racing, because the cars don't travel at a constant velocity. Work on getting a smooth panning motion. The exact rate that you pan will be depending on the speed and acceleration characteristics of the cars you are shooting. You'll be panning much faster with Top Fuel than with Pro Stock for instance.
Once you are comfortable tracking the subject, start taking pictures. If you are having trouble speed up your shutter. Or consider using a mono-pod if you are unstable. Or try keeping both eyes open while you are shooting.