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A speeding motorist passes a motorcycle policeman parked beside the road. The policeman begins pursuit at the instant the speeder passes him. The position of the speeder with respect to the starting point of the policeman is given by: x = 30t. The policeman accelerates in a way such that his position with respect to his starting point is given by: x = 2t2. For both objects the time is measured in seconds and the position is measured in meters.
Find the time at which the policeman catches up to the speeder.
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