There are two options available to you that will each give a 'different' type of blur.

a) You can simply use a high shutter speed, that necessary to freeze the motion of the vehicle, and a wide aperture. This gives normal out of focus blur to the background/foreground.

or

b) You can 'pan' the vehicle, moving your camera to follow the vehicle, and using a 'slower' shutter speed to give motion bur to everything but the vehicle. Personally I find this best done handholding the camera, a tripod/monopod being a hindrance. These cars were fast, for slower cars a slower shutter speed say 1/60s you may find preferable.

Here's a couple of examples,

There are two options available to you that will each give a 'different' type of blur.

a) You can simply use a high shutter speed, that necessary to freeze the motion of the vehicle, and a wide aperture. This gives normal out of focus blur to the background/foreground.

or

b) You can 'pan' the vehicle, moving your camera to follow the vehicle, and using a 'slower' shutter speed to give motion bur to everything but the vehicle. Personally I find this best done handholding the camera, a tripod/monopod being a hindrance. These cars were fast, for slower cars a slower shutter speed say 1/60s you may find preferable.

Here's a couple of examples,

When I taught PANNING I recommended that my students practiced moving there camera side to side and tripping the shutter while CONTINUING THE PAN and not stopping the camera during the pushing of the shutter. That is the most important thing about shooting while panning, do not stop your movement while pressing the shutter.
You can use any slow shutter speed you want. The slower the shutter, the more background blur you will get, and the slower the shutter, the more your main subject will show movement. Your job is to find that balance between shutter speed, subject speed, and background blur.
I suggested my students use shutter speeds of 1/15 to 1/60 sec. and see what shutter speed they liked best, your effect will also depend on the speed of the subject, the faster the subject, the greater the background blur because you are panning more quickly to keep up with the subject, also depends on how close you are to the moving subject. Also the effect depends on the lens you are using, wide creates an interesting blur, but you should be close.
And to be honest, everyone will have there own favorite blur.
Below is an image of a king fisher in a full out dive, they dive very quickly, the lens was a 600 mm and I was shooting at 1/2000 sec. but the background blur was created by the speed of the Kingfisher and the distance of the background from the subject. There are so many variables that experimenting is sometimes the best way to do it. I would suggest a digital camera as you can see the results right away.
I also suggest you get a volunteer to run past you at various speeds and you at various shutter settings. If your shooting film you must record you shooting data yourself, if your shooting digital this information will be recorded for you.
Good luck and keep on shooting until the end.

When I taught PANNING I recommended that my students practiced moving there camera side to side and tripping the shutter while CONTINUING THE PAN and not stopping the camera during the pushing of the shutter. That is the most important thing about shooting while panning, do not stop your movement while pressing the shutter.
You can use any slow shutter speed you want. The slower the shutter, the more background blur you will get, and the slower the shutter, the more your main subject will show movement. Your job is to find that balance between shutter speed, subject speed, and background blur.
I suggested my students use shutter speeds of 1/15 to 1/60 sec. and see what shutter speed they liked best, your effect will also depend on the speed of the subject, the faster the subject, the greater the background blur because you are panning more quickly to keep up with the subject, also depends on how close you are to the moving subject. Also the effect depends on the lens you are using, wide creates an interesting blur, but you should be close.
And to be honest, everyone will have there own favorite blur.
Below is an image of a king fisher in a full out dive, they dive very quickly, the lens was a 600 mm and I was shooting at 1/2000 sec. but the background blur was created by the speed of the Kingfisher and the distance of the background from the subject. There are so many variables that experimenting is sometimes the best way to do it. I would suggest a digital camera as you can see the results right away.
I also suggest you get a volunteer to run past you at various speeds and you at various shutter settings. If your shooting film you must record you shooting data yourself, if your shooting digital this information will be recorded for you.
Good luck and keep on shooting until the end.