From my experience, I can tell you that resting is the most important aspect of a successful journey. Make sure that you're well rested before you set off. 24 Hour drive isn't really that long but since you mentioned you're traveling alone, it could be turn out to be really long.

Try to drive through entire North Dakota without making a single stop and after that, I'd suggest you to stay in a motel in Montana ( you don't necessarily need to book a room ). Also, set off at around 10 am. That's the best option because you can drive all day, stay overnight in a motel and then set off again.

Burn cds and when you stop in a gas station for gas, rest for 10-15 minutes, stretch!

Also, Red bull is your best friend! Don't "overdo" it though because it will lose its effectiveness.

Good luck!