If you're prompt, you're on time. Go ahead and be prompt to class. Also, to prompt is to inspire or make happen. Getting in trouble for being late should prompt you to get a better alarm clock.
The adjective prompt can mean "as scheduled," or simply "quick." When you prompt someone, you motivate them in some way: you might offer a reminder, assistance, or even inspiration to do something. For example, honking your car horn prompts your friend to get moving, and speaking up in defense of your classmate might prompt a bully to change his ways. If a director prompts an actor who's forgotten his lines, she reminds him what comes next.