Braswell played in 10 games in 1974 as a freshman, catching 28 tackles. In 1975 Braswell was the No. 2 defensive end behind Buzzy Thornton. He started 10 games in 1976 and had 62 tackles this year. In 1976, he returned to the Mountaineer squad after missing the previous season due to a knee injury and operations. Braswell was the number one linebacker with Jeff Macerelli, but moved to linebacker from defensive end in the spring. His brother Chuck was a starting cornerback for the Mountaineers. Ken majored in general studies.

He was All-WPIAL at Clairton High School. Ken was lettered in football, basketball, and baseball. WVU Coach Cignetti mentioned that "Ken has potential to be an excellent defensive football player; he has good quickness and the ability to get the ball quickly."