Carmageddon (and 2) seemed to have a physics engine qualitatively different to the modern norm, seemingly modelling the time of impact and the impulse response to that, rather than correcting everything after intersection has already happened. It also seemed to have different static and sliding friction and modelled air friction and wheel dynamics to the extent that a power-up increasing acceleration and grip could make your car flip up like a hot rod.
It made a huge difference to the feel of the physics and made things far less springy and slippery than box3d, havok and almost every modern game that uses a dynamic physics engine.
This did mean that you could sometimes do things that made the physics take a noticeable amount of time and cause lag, but it also made things feel far more real than any physics engine I've seen since.
Hopefully, someone will be able to reproduce that, now.
Edit: I believe it even incidentally reproduced the intermediate axis theorem [1] on cars spinning through the air, presumably as an emergent phenomenon, which I've not seen any other physics engine do.