The incident happened shortly before 5 p.m. at New York Avenue and Avenue J in Midwood.
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Police say they tried to stop a white Mercedes-Benz along Flatbush Avenue, but the driver of the car took off on Avenue J, blowing through stop signs before striking the family.
The mother had been waiting for two of her four kids to get off the school bus at the time of the incident.
"When the Mercedes hit the woman, the woman flies and hit the ground and the kid was shivering," one witness said.
The five victims were taken to a nearby hospital in stable condition, and they are all expected to survive.
The victims included a 41-year-old mom, 1-year-old daughter, 3-year-old son, 5-year-old daughter and an 8-year-old daughter.
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The 8- and 5-year-old went to an all-girls private school called Beth Jacob.
Police found the car a short distance away at E 24th St and Glenwood Road.
Police sources say the female driver abandoned it there and walked away.
No one has been arrested.
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