ATLANTA — From beginning to end, the encounter between Rayshard Brooks and two Atlanta police officers lasted 41 minutes and 17 seconds. For the first 40 minutes, it looked like a textbook example of policing.

The officers treated Mr. Brooks, 27, with respect. They were cordial as they asked about his night and how much he had had to drink. They calmly guided him through a series of sobriety tests.

Then things went dangerously awry, and Mr. Brooks became yet another African-American man to die at the hands of the police.

The encounter — veering from calm to fatal and captured on video from multiple angles — has become the subject of intense scrutiny. There is vigorous debate over a host of decisions, big and small, that the two officers made last Friday night in a Wendy’s parking lot, where Mr. Brooks had fallen asleep in the driver’s seat in the drive-through lane.

“It’s at the point where the officer places his hands on him that things go south in a fraction of a second,” said Kalfani Ture, an assistant professor of criminal justice at Quinnipiac University who said he had viewed the video footage more than three dozen times. “So you have to pay attention to the minutiae of details — you have to try to understand decision-making, but you also have to pick out best practices.”

Understanding what went wrong, he said, is a crucial step in helping the police do their jobs better and ease tensions with communities of color.

As the officers moved to arrest Mr. Brooks, whose Breathalyzer test registered a .108, above the legal limit to drive in Georgia, he bolted from their grasp, hit an officer, grabbed the other’s Taser, fired it, and took off running.

Officer Garrett Rolfe discharged his own Taser and reached for his 9-millimeter Glock handgun as Mr. Brooks turned and discharged the stolen Taser again. Officer Rolfe fired, striking Mr. Brooks twice in the back.

Mr. Brooks was 18 feet and 3 inches away when the first shot was fired. Prosecutors said that as Mr. Brooks lay dying, Officer Rolfe kicked his bleeding body and the other officer, Devin Brosnan, stood on his shoulder. Neither offered medical assistance for more than two minutes, prosecutors said.

On Wednesday, the Fulton County district attorney, Paul L. Howard Jr., charged Mr. Rolfe, who had been fired from the Atlanta Police Department, with 11 criminal counts, including murder and aggravated assault. Officer Brosnan, who is on administrative duty, was charged with three counts, including aggravated assault and violations of oath.

The decision to file charges came five days after the fatal encounter, which has led to the resignation of the city’s police chief and the mayor’s announcement of a series of measures to overhaul how and when police officers use force. The shooting came amid nationwide protests over police brutality and systemic racism that followed the death of George Floyd in Minneapolis.

President Trump weighed in briefly this week, telling Sean Hannity of Fox News that people should not resist police officers. He also said he hoped Mr. Rolfe “gets a fair shake because police have not been treated fairly in our country.”

Some observers have said the shooting death of Mr. Brooks could have been avoided if the two officers, who are white, had declined to arrest him. According to the footage from Officer Brosnan’s body camera, Mr. Brooks maintained that he had not had more than two drinks that night.

But he also made a suggestion: “I can just go home.”

It seemed like a simple request. “Why didn’t they just let him go home?” Mr. Brooks’s father, Larry Barbine, asked in an interview with The Toledo Blade.

Dr. Ture, a former law enforcement officer, said he likely would have written a citation but not taken Mr. Brooks to jail, particularly given the presence of the coronavirus in many detention facilities.

“I’d have said, ‘Mr. Brooks, I’ll offer you a ride wherever you want to go, however, I’m going to take your vehicle keys,’” Dr. Ture said. “If I was so concerned I might even tow the vehicle. But I might not even take Mr. Brooks to jail.”

But other experts said that for decades, the police have been told that society wants law enforcement to take a zero-tolerance approach to drunken driving, the No. 1 cause of death on U.S. roadways.

“Like with so many other social problems, we put officers at the forefront of dealing with D.U.I.,” said Seth Stoughton, a former police officer who teaches law at the University of South Carolina. “So it should be no surprise that officers arrest someone for D.U.I. That’s what we’ve been telling them to do for a long time.”

Vince Champion, the southeast regional director for the International Brotherhood of Police Officers, the Atlanta police union, said there were limits to an officer’s discretion.

Mr. Champion said he once let an inebriated driver walk home a short distance and the man was struck and killed. His supervisor, who had approved the move, was demoted, he said. Such episodes can lead to lawsuits.

“We’ve had to go away from trying to be nice,” he said.

After Mr. Brooks went through a field sobriety test and the Breathalyzer test — both of which came after he was unable to identify which county he was in and gave a seemingly implausible explanation about how he had arrived at the Wendy’s — Mr. Rolfe decided to arrest him.

“All right, I think you’ve had too much to drink,” he said, moving to cuff Mr. Brooks, according to the video footage. “Put your hands behind your back for me.”

In his news conference announcing the criminal charges against the officers, Mr. Howard said they had violated the Police Department’s policy because Mr. Brooks “was never informed he was under arrest for driving under the influence.”

Verbally notifying people that they are about to be arrested accomplishes multiple goals, experts say. It is a way to show respect and courtesy, which increases public confidence in the police. And it is also tactical — it helps slow the interaction down to eliminate surprises.

When people are not told what to expect — particularly intoxicated people — they can react in ways that an officer might misinterpret as resisting, when in fact the person is simply startled.

“In many situations, officers should tell someone what is happening because you don’t want the person to react in surprise and the officers to take that surprise as resistance,” Professor Stoughton said.

When Mr. Brooks lurched away from the two officers as they moved to cuff him, they hung on, and the three fell into a heap on the pavement, fighting and struggling.

Video footage shows Mr. Brooks seizing a Taser from Officer Brosnan, and striking Officer Rolfe. In a statement this week, the lawyers representing Officer Brosnan said Mr. Brooks used the Taser on their client at around this point.

After a few moments, Mr. Brooks broke free of the officers. As Mr. Brooks ran away, Officer Rolfe fired a Taser at him, a violation of department rules that prohibit firing at a fleeing suspect, prosecutors said.

Seconds later, mid-stride, Mr. Brooks turned and fired the Taser at Officer Rolfe, who was close on his heels.

Three gunshots can be heard, and Mr. Brooks falls.

Mr. Howard said that Officer Rolfe, before opening fire, must have known that the Taser that Mr. Brooks had taken had already been fired twice — and that this model of Taser was only capable of two shots.

Several policing experts agreed that Officer Rolfe should have known that Mr. Brooks was not a deadly threat, but for other reasons.

Mr. Brooks was running, and it seemed like escaping the situation was his only goal, some experts said. And although Georgia officers are taught that Tasers are a deadly threat because they can disable officers long enough for their guns to be seized, that threat is diminished when a second officer is present as backup.

Use of force should be proportional to the threat, the experts said.

But whether the officer should have known how many times the Taser had been fired — or could have reacted quickly enough to that knowledge — was a separate question.

“That’s a high expectation in the middle of a fight, that an officer is going to know every single fact that we get to see after the fact with an analysis of the video,” said Roberto Villaseñor, a former police chief in Tucson, Ariz., and a member of former President Barack Obama’s Task Force on 21st Century Policing.

“There’s a lot of things that occur in a dramatic, volatile situation that you might not be aware of,” he continued. “You have adrenaline pumping, you’ve got fear working, you’ve got the fight-or-flight syndrome going on — you’ve got a lot of things that are affecting your perceptions.”

Noah H. Pines, a lawyer for Mr. Rolfe, said in a statement this week that the shooting was justified, and that the responsibility was squarely at Mr. Brooks’s feet.

“When Mr. Brooks chose to attack two officers, to disarm one of them,” Mr. Pines said in the statement, “he took their lives, and his own, into his hands. He took the risk that their justified response might be a deadly one.”

But on CNN on Monday, Stacey Abrams, Georgia’s former Democratic candidate for governor, called it “murder.”

“At no point did he present a danger that warranted his death,” she said of Mr. Brooks. “And that’s what we’re talking about. A murder because a man made a mistake, not a mistake that would have cost the police officer his life but a mistake that was caused out of some form of dehumanization of Rayshard Brooks.”