Here are 3 possible expressions of relief for the situations:
1. You say to your mother "Thank goodness I've finished all my homework, especially the math assignment. It was such a relief to get it done."
2. You say to the person on the bus "Whew, I'm so relieved we aren't late. That would not have been good since the teacher is very strict about tardiness. It's a relief to make it on time."
3. In response to doing well on a difficult test, you say "I'm really glad I studied hard for this test. It was challenging but I'm relieved I think I did well. What a relief to be finished!"