Expressions: Open up, wait up, etc


Could you please tell me why and when we use up with the following verbs?

1- Hey, open up!
2- Hey, wait up!

I would be obliged if you could give me a few more examples of the same sort!


A few examples:

After a lot of careful prodding, she finally opened up and told me what was troubling her. (open up = stop hiding feelings/speak openly and honestly)

They opened up a new business last week.

I bought a Porsche yesterday and I could hardly wait to get on the autobahn and open it up. (open it up = drive at high speed)

I waited up for him so that I could give him the news as soon as he got home. (waited up = I didn’t go to bed)