Mark Treyger's proposed law would make New York City the largest in the nation to ban the practice.
The driver was behind the wheel of a gray 2013-2014 Ford Mustang, police said.
Residents say the entrance is dangerous for straphangers due to poor visibility and speeding vehicles.
The DOT says that 155th Street near Edgecombe Avenue is one of the city's most dangerous intersections.
A pedestrian was struck by a motorcyclist at 42nd Street and Fifth Avenue, police said.
A 58-year-old woman is in critical condition after a cyclist hit her Thursday afternoon in the park.
Irving Schachter, 75, was training for a marathon when he was hit by a biker, police said.
Jean Chambers was hit by an SUV while crossing West 95th Street at West End Avenue.
Enforcement of the new rule will begin July 7, police said.
A 74-year-old woman was seriously hurt by a CitySights NY bus at Seventh Avenue and West 14th Street.
Helen Rosenthal wants to extend "Cooper's Law" to cover all New York drivers.
The blitz at 74th Street and Roosevelt Avenue is part of the mayor's Vision Zero pedestrian safety push.
The 24th Precinct also went on a ticketing blitz targeting drivers who failed to yield.
Shear was struck and killed by a vehicle on the Upper West Side Friday.
The woman was taken to Weill Cornell Medical Center, FDNY officials said.
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