Beat some of the specific courses and you will unlock these videos.

Prize	How to unlock
Prize 02 Rage Racer Opening Video	Beat all courses in E40
Prize 03 R4 Opening Video	Beat all courses in E41
Prize 04 2004 E3 Video	Beat all courses in E45
Prize 05 Ridge Racer Opening Video	Beat all courses in E46
Prize 06 2006 E3 Video	Beat all courses in E47
Prize 07 Yamasa Raggio Movie Video	Beat all courses in E48