Without any scientific evidence to back it up, I would expect that this is a result of the relative speed of different parts of the cars across the frame. If you notice, the shots that you took parallel to the cars have the entire car in focus. The ones exhibiting partial blur have the car approaching at an angle.
The close distance that was necessary to use use that relatively wide lens would increase this effect. The closer you are to an object, the faster it will travel across the frame of a photo. Therefore, a closer object requires a faster shutter speed to stop the action. When you are as close as you were to a speeding car, even though the entire car is moving at the same speed, the portion closest to the camera will move across the plane of the photo frame faster that the more distant portions.
I have taken many waterfall photos, and quickly became aware that, in order to get the same amount of blurring in falling water, I would have to increase my shutter speed as I moved closer to a waterfall.
Think of shooting an airplane in the sky. Assume that you are using the same focal length for two shots of the plane. In the first shot the plane, the plane is at a distance such that it is a small detail in the sky. It would be easy to have the plane appear sharp, and, at sufficient shutter speed, it could appear relatively sharp without the necessity of panning. In the second shot, the same plane, travelling at the same speed, passes by at just 50 feet in front of you. You would be hard pressed to capture that plane as anything but a blur.
I thnk that you are experienceing the same effect. You shot from close enough to the car, and at a sufficient angle, to record the fact that the front on the car, being closer to the plane of your sensor, was actually moving faster across the frame than was the middle of the car.
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Cliff
http://www.pbase.com/cliffb 
