A motorized bicycle or moped cannot travel faster than: Do you currently have car insurance? Insurance is mandatory to drive in Ohio Yes I have insurance. But please show me your best quotes. No, please help me find the best insurance. Question A motorized bicycle or moped cannot travel faster than: Answers 25 mph. 30 mph. 35 mph. Explanation In California, a motorized bicycle or moped is defined as a two- or three-wheeled vehicle that is capable of traveling at speeds no faster than 30 miles per hour on level ground. This questions appears in the following tests: California Motorcycle Practice Test 29