Federal prosecutors on Wednesday opened their case against three former Memphis police officers involved in the fatal beating last year of Tyre Nichols, a 29-year-old FedEx worker, accusing them of having doled out the blows to punish him for leaving a traffic stop.

It was the “run tax,” said Elizabeth Rogers, an assistant U.S. attorney, using what she said was internal Memphis police slang for the punishment delivered to anyone who fled — extra punches or kicks that would never be reported.

The lawyers of the three former officers — Tadarrius Bean, Demetrius Haley and Justin Smith — instead framed the fatal encounter as the unintended consequence of a chaotic stretch for a group of officers tasked with policing high-crime areas of the city. They said that the officers had responded in line with their training to someone who did not answer to their commands and ran away.

The former officers face charges of violating Mr. Nichols’s civil rights and conspiring to lie about what happened, and could face life in prison if convicted. Mr. Nichols, who is Black, died on Jan. 10, 2023, three days after the beating from the officers, all of whom are also Black.

After Mr. Nichols’s death, hours of video footage were released that showed officers kicking and punching him even as he showed little resistance, horrifying the city of Memphis and the nation. Several other officers and emergency personnel were fired, including two officers, Emmitt Martin III and Desmond Mills Jr., who pleaded guilty to federal charges.