Now officers are appealing for witnesses to come forward after the pursuit on the A1M.
At around 4.25pm, officers began following a grey Audi A4 that failed to stop for them on the north-bound carriageway near Catterick.
The vehicle continued north through roadworks before leaving the motorway at Scotch Corner, then returned to the A1, on the south-bound carriageway.
The car continued south at speeds of more than 100mph, weaving in and out of traffic and onto the hard shoulder.
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With the assistance of the National Police Air Service, officers stopped the vehicle on the exit slip road of the A1 near Boston Spa. A man aged 31 and a 22-year-old woman aged 22, both from Rotherham, were arrested at the scene. They remain in police custody.
Police recovered a large quantity of suspected cannabis from the vehicle and also found a three-year-old child was also inside the vehicle.
Police say some motorists who witnessed the suspect vehicle's manner of driving have already come forward and officers are appealing for any others to come forward, including any that were hit by the vehicle.
Anyone who has not yet spoken to the police is urged to call North Yorkshire Police on 101, select option 2 and ask for Harrogate Serious Crime Team.
No-one was injured in the incident.