Battle Out Run is Sega's answer to Taito's Chase H.Q. You drive a red sports car and must apprehend eight target vehicles in selected cities across the USA, including Los Angeles, Chicago, Miami, and New York. You have to do this while avoiding yellow cars and other obstacles. Halfway through the eight stages, you enter a shop that allows you to upgrade your car and get some nitros, as long as you have money, and you will be rewarded if you apprehend the vehicles. This can be done by bumping into them to disable them.
source: www.mobygames.com/game/sega-master-system/battle-out-run