Kevin O’Connell, 33, of Slater Crescent, Wirksworth, had intervened in an argument between two people on Burton Road, Derby, just before 1pm on Saturday.
Sergeant Darren Muggleton, of Derbyshire police, who is investigating the incident, said: “We are in the early stages of the investigation but it appears that Mr O’Connell had stopped his car to try to break up a disagreement between two men.
“One man ran off and Mr O’Connell was chasing him when he fell into the path of a car that was passing.
“This tragic incident was witnessed by his three children. He died a hero trying to help a member of the public he thought was being victimised.”
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Officers have spoken to several witnesses and are conducting house to house enquiries to gather information about exactly what happened.
Two men, aged 27 and 34, who were involved in the argument, were arrested on suspicion of assault on each other and were bailed after being questioned.
Anyone who witnessed the incident should contact Sergeant Muggleton on 101