Which vehicle is specifically designed for conveying one or more persons and typically has a maximum speed of 15 mph?

The vehicle that is specifically designed for conveying one or more persons and typically has a maximum speed of 15 mph is a golf car or golf cart. These vehicles are primarily used for transporting players and their equipment around a golf course, but they can also be utilized in other settings, such as gated communities or large private properties.

Golf cars are designed with a low-speed capacity to ensure safety in environments where pedestrians are present, thus making them distinct from other vehicle types. In contrast, motorcycles, motor-driven cycles, and mopeds are typically capable of higher speeds and are regulated differently in terms of licensing and operation on public roads. The primary function and speed rating of golf cars directly align with the characteristics outlined in the question, confirming this answer as the most fitting option.