On March 16, 1995, about 1700 eastern standard time, a Cessna 172, N65490, operated as a rental/instructional airplane, landed long and ran off the runway at Gratiot Community Airport in Alma, Michigan. The airplane sustained substantial damage when veered off the left side of the runway, then nosed over. The Certificated Flight Instructor and Private Pilot on board the airplane reported no injuries. Visual meteorological conditions prevailed for the instrument training flight, no flight plan was filed. The dual instructional flight operated under 14 CFR Part 91, and originated from Pontiac, Michigan, approximately 1600. The flight instructor reported the dual student was manipulating the airplane controls when they attempted to land on Runway 9 (5,000' X 75', asphalt.) He stated when the airplane touched down, it pulled sharply to the left. The flight instructor took over the controls, but was unable to stop the airplane from veering off the left side of the runway. The airplane came to a stop nose down in the soft ground. The flight instructor's written statement indicated there was a mechanical malfunction/failure of the left brake. Postaccident investigation revealed no evidence of mechanical difficulty with the brake system. A Gratiot Community Airport employee observed the wind was out of 260 degrees, "...with occasional southerly shifts..." at an estimated 9 knots at the time of the accident. He stated local traffic had been using Runway 27 for takeoffs and landings that afternoon, but there was a "lull" in the traffic when the accident airplane arrived. The airport employee stated when he observed the airplane it seemed high and fast on final for Runway 9. He reported when the airplane passed the midpoint of the runway about 50 feet above the ground and still fast, he commented to a friend "...this would be a good time for a go around." The airport employee estimated the airplane touched down about 1,000 feet before the departure end of the runway, then veered off the left side of the runway and nosed down.