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A 32-year-old motorist is being quizzed by police on suspicion of driving at pedestrians before later crashing into parked cars.
The alleged incident happened just after midnight in Peacock Street, Gravesend.
Police spokesman James Walker said the force received a report that a motorist had driven aggressively towards two or more people. No injuries were suffered.
After leaving the area, the motorist is then reported to have been in collision with a number of parked vehicles.
Following a search of the area, a 32-year-old man from Gravesend was arrested at a private address in York Street.
He was arrested on suspicion of assault, criminal damage and driving under the influence of drink or drugs and remains in custody as inquiries continue.