Video shot by a witness shows smoke rising from car as it appears pinned beneath the train.
The exact cause of the collision is under investigation.
Amtrak officials say the train was traveling between San Jose and Oakland when it struck the car.
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They say the car was illegally on the tracks.
None of the passengers were injured though the train was evacuated, Amtrak says.
Amtrak says it is providing alternate transportation for customers to stop at Oakland Coliseum/Airport, Oakland Jack London Square, and Emeryville; the remaining passengers will be transferred to another train.