In case after case, it took only a split second for an officer to pull the trigger.

Adam Toledo, a 13-year-old in Chicago, had tossed away a handgun and begun raising his hands. Ma’Khia Bryant, a 16-year-old in Columbus, Ohio, lunged with a knife at another teenager. Tyrell Wilson, a 33-year-old mentally ill homeless man in Danville, Calif., had a knife in hand when he shouted “Kill me” at an approaching deputy sheriff.