Super Chase H.Q. (Game Boy)

At the start of each level the player is informed who they are pursuing, a great distance away: They must apprehend the criminal before their time limit expires. The criminal's car is constantly moving away, so if the player repeatedly crashes or drives too slowly, the criminal will escape. At some points during the game the road splits, and the correct turn must be taken, otherwise it will take longer to catch the criminal. When their vehicle is reached, the time limit is extended; the vehicle must be rammed a number of times until the criminal is forced to stop, then is arrested.

Source: Wikipedia, "Super Chase HQ", available under the CC-BY-SA License.