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A 34-year-old was arrested after police officers were called to a collision at junction 6 of the M2 motorway near Faversham on Tuesday.
The man, from Whitstable, was held on suspicion of possessing an offensive weapon, driving while unfit through drink or drugs and possession of drugs.
Police seized what they believe to be cocaine and cannabis from the scene.
The man has been bailed by police at Sittingbourne pending further enquiries.