The student pilot stated that he was conducting his second solo flight. After performing maneuvers in the practice area, he returned to the airport to conduct takeoffs and landings. The student pilot stated that, after the second landing, he was "in a hurry" to exit the runway and attempted to depress the brakes "all the way." The airplane "turned to the right," travelled into a grassy area on the right side of the runway, and impacted a taxiway sign, resulting in substantial damage to the left wing. Postaccident examination by a Federal Aviation Administration inspector revealed no mechanical malfunctions or anomalies.