[rasz_pl]

this feature is literary called "Catch Up" https://en.wikipedia.org/wiki/Game_mechanics#Catch-up and has been a thing in racing games since before 2000. Diddy Kong Racing (1997) had it, so did motorhead in 1998, then EA got familiar with it and we got Hot Pursuit 2/Most wanted and burnout 3.

[softawre]

The original Mario Kart did this with the strength of Powerups (and maybe speed as well?)