Not quite PS2 but can give you actual lap speeds.

We have had over 20 play it at one time.

Nearly 30 years old, so please try it and let me know your lap times and speeds. It is easy to reproduce (the game I mean !)

http://www.bbhmg.com/2006tt.htm

Invented, designed and produced by IHBBHMG/GOOD GAMES of Reading

Nice one Ian, I have notified a few others about this gem of a game, I hope that there is a revival forthcoming.