I shot Indycars for 6-7 years back in the early 1990's.
I learned to shoot at about 1/30th or less (for artsy shots) with reeeeeeeally steady motion, without regard for aperture, to 1/200th (juuuust that little bit of motion or when they're at full song) with the smallest apertue I could get by with. On one occasion the sun was perfect but my backdrop had a trackside porto-san in it: I shot f2.8 with ND filters to slow my shutter, and blurred it away.
The difference in blur, front to back, is caused by your panning actions themselves. The kart looks like it's on a straight, and you are panning, right to left. The camera is turning, the car isn't, and something's gotta give - in that case it's the front of the cart. Additionally, you might be moving your body withut knowing it - that causes all manner of things like up and down blur in odd places. Maybe you took an involuntary breath. Photogaphers move a LOT when panning shooting race cars.
Tip: shooting from the apex of a corner and panning gives really smooth results - you're turning, the car's turning, life is good. I always did better with a longer lens from a distance - I could control my body rotation more.
Incidentally - that shot is quite good - go look at RACER or Road and Track and check their action/blur shots - this pic, if it was Hamilton, Andretti, or Tracy could keep up with the big boys and make a sale...too bad the sun wasn't out, though.
I sold the one below to On Track magazine in 1992 or 93 - shutter was something like 1/30 - it was the title shot for the article on Kim Green's racing team.
Not a great scan, and not a particularly good shot, but see the difference in blur from the front to back tires? He went by me at an angle, about 90MPH, headed uphill to pit. Wierd angle to pan, and in the end I love the effect. The reason they liked the shot was because I missed my subject: I was shooting for Jaques' distinctive helmet, but his dad's car number (27) came in focus - the editor liked that. Funny how that works.
And the trick, when they're moving at 185 to 225 mph is similar to what Village said: start tracking early, as soon as you can, and (depending on shutter lag - cars could go 10-15 feet or so with my old film cameras) release the shutter
just before the feature you're shooting for (helmet, for open wheels, driver or rider body for karts and bikes, sponsor name if you're on assignment) gets there. Keep the center focus on the feature, do NOT autofocus (nice thing about racing: they go by almost the same way every time. Lots of setup time available). Crop later.
And Double H - I shot NHRA twice and didn't sell a thing: drag racing was HARD to shoot! Your shots are lovely!
Cheers