A speeding hit-and-run driver killed a 28-year-old nurse walking home from working the overnight shift at a nearby Brooklyn hospital on Saturday, according to officials and video of the crash.

Jiayi Zheng — still wearing her forest green scrubs — was walking along the crosswalk at 55th Street and Third Avenue when the operator of a black Cadillac sedan drove through a red light and barreled into her around 7:30 a.m. in Sunset Park, disturbing footage shows.

Zheng was sent flying in the air before landing on the median, just a block away from where she worked at NYU Langone-Brooklyn Hospital as a medical- surgical unit nurse.

Medics rushed her…

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