John Jerome Smith, 54, a physical education teacher at Stanton Elementary School in Washington for about 15 years, died Sunday at Alexandria Hospital of injuries suffered April 5 when he was struck by a car on Jefferson Davis Highway near his home in Alexandria.

A resident of the Alexandria area for 28 years, Mr. Smith was born in Pensacola, Fla. He graduated from Tuskegee Institute with a degree in physical education. he also played football, baseball and tennis there. Later he took graduate work at Howard University.

In 1957, Mr. Smith taught physical education at Douglass High School in Leesburg, where he coached the football and baseball teams.

He then taught physical education at Luther Jackson High School in Falls Church. In 1959, he was named head of atheletics at the 12th Street YMCA in Washington, where he remained until becoming an instructor at Stanton School.

Mr. Smith was a member of St. Joseph Catholic Church in Alexandria.

he is survived by his wife, Marion Beatress Smith, a daughter, Lisa Maldosia, and a son, Kenneth Oswell, all of the home; his mother, Irene Smith, of Lees, Ala., a brother, Robert of Gary, Ind.; a sister, Delores Glenn of Youngstown, Ohio, and one grandchild.