Moses was shot and killed by New Castle County Police on January 13.
Police body cam video shows the encounter along Rosemont Avenue in Wilmington.
Investigators say Moses took off, made a U-turn and then drove at a high rate of speed towards the officers.
That's when police say they were forced to fire their weapons.
The family contends that Moses was trying to get away and not driving towards the officers.
The Delaware chapter of the NAACP wants a rush on the investigation.
"Provide the full, unedited, video and audio of the body-worn footage; determination of the officers who fired their weapons; and for the officers to criminally be prosecuted here in the First State for Mr. Moses," said Coby Owens of the Delaware NAACP.
Moses' family members said they will keep protesting until they have more answers.