It happened just before midnight Tuesday underneath the Route 64 Bridge just north of Washington Road at the Princeton Junction Train Station in West Windsor.
Police arrived to find the disabled 2012 Toyota Camry facing east on the westbound Amtrak track.
They say the vehicle had been driven by 23-year-old Amna Ahmed, who was at the scene along with her father and sister, who had arrived to provide her with assistance and were parked on an access road next to the train tracks.
Despite efforts to stop all train traffic in the area, police say a westbound Amtrak train approached at a high rate of speed as officers and the family scrambled for cover.
The train destroyed the Toyota and sent debris flying toward the area where the officers had just been standing.
Two police cars were also damaged, one extensively, as was the car driven by Ahmed's family. The train and numerous other trailing train cars were also damaged.
No injuries were reported, but the incident disrupted traffic in the area for hours.
Authorities said Ahmed was determined to be intoxicated at the scene and was issued summonses for reckless driving and DWI.