Presumably there will be other vehicles on the track, so the means must involve something that either won't detect other vehicles, or will discriminate between them.
I guess there are plenty of safety standards that limit what you can place around the track near where the vehicles might be, so preferably it needs to be able to detect the vehicle at a distance.
One option might be to attach a small transmitter to the vehicle and then determine using the Doppler effect, whether the vehicle is approaching or receding from the receiver.
If you can detect the rate of change of frequency, the time when the vehicle is closest to the sensor is the time when that rate of change passes through zero (and changes sign).
This would need to be tested to ensure that it detected the vehicle at the same point whilst it was travelling at different velocities, was under acceleration, or took a different line, or if it was in traffic.
Another option might involve cameras and detecting the vehicle, however this might fail if you have more than one car that looks similar (as I guess team cars tend to do). The other issue with cameras is that you need to find somewhere to place them.
Have you tried GPS receivers? Even if you can get a position only every second, you should be able to interpolate. Of course this would be very sensitive to acceleration. Perhaps it could be augmented by a pair of sensors that track acceleration in 2 axies. This should allow a better "dead reckoning" between GPS updates. This could be the core of an inertial position sensing unit which could be placed on the car allowing it's position to be accurately reported with the other telemetry that you doubtlessly stream from the car (in fact you may already track acceleration). It would be a lot neater if the car could generate its own splits -- makes it easier to set up a new track too, just drive around it (in another vehicle if you need to) and press a button to tell the device where you want splits.