The student pilot stated that after takeoff during his second supervised solo flight, he remained in the traffic pattern and landed uneventfully, but during the landing roll elected to perform a touch-and-go landing and applied power. Immediately after adding power, the airplane turned left and he used rudder to correct the left turn but then decided to perform a full stop landing. He applied the brakes in an effort to keep the airplane on the runway, and reduced power, then added a little power inadvertently because he was nervous, then reduced power. The airplane departed the runway, and went into water while traveling about 30 knots. The student pilot further stated there was no preimpact mechanical failure or malfunction. The students’ certified flight instructor stated that after veering to the left, the airplane exited the runway onto grass, crossed runway 25, and then went into a ditch at which time he heard power applied. He then watched the airplane travel into the water and ran to the airplane to assist his student. Postaccident inspection of the flight controls by a Federal Aviation Administration airworthiness inspector revealed no evidence of preimpact failure or malfunction.