On April 19, 1995, at 1650 central daylight time, a Beech B19, N1967W, registered to an individual, and operated by a student pilot overran runway 35 (2,400' x 40' dry/asphalt) at North Omaha, Nebraska. The airplane sustained substantial damage. The student pilot reported no injuries. The 14 CFR Part 91 solo instructional flight was being conducted in visual meteorological conditions. No flight plan was on file. The local flight departed at 1600. The pilot stated that due to turbulence on base leg and final approach he landed long and flared late. He said he felt that he did not have room left to abort the landing and applied brakes in an attempt to stop on the runway, but was unable to do so. The pilot stated that there was no mechanical malfunction with the airplane. A post accident examination failed to reveal any pre-existing mechanical anomalies.