I think Romeo’s actions are believable if we recognize that he is a fickle youth. Just a short time before he saw Juliet he was in love with Rosaline. In fact Father Laurence chided him about his rapidly changing emotions.
I think you may want to look for any accounts- historical or literary, that could shed light on the life of young people during Shakespeare's time.
This may reveal some further insight into the behavior of Romeo, and that of Juliet as well.
The subjectivity of this question leads one to believe that an opinion is being sought rather than hard facts. Here's the bottom line: If you consider it believable that a boy (or a girl) would abandon his family's wishes to seek out true love, then yes, his actions in this entire play are believably motivated. However, if you believe (in contrast) that no one would go so far for the sake of a relationship in this day and age, then perhaps your answer is no. In the end, the answer depends entirely upon your perception of the story and its plot. You may wish to ask your teacher for some clarification of the question itself.
You need to be more specific about which actions you mean. Does it seem believable that Romeo would, upon seeing Juliet from across the room, lose all interest in Rosalie, for whom just moments before he was professing undying love? Possibly, given that he was a young teenager (think of your own friends - does this seem believable in today's high school?) Would his actions of running away when accused of murder seem reasonable and believable? I'd say so. I think most reasonable people would want to flee if a bounty lay upon their head! What about the final act of taking his own life when he believes Juliet to be dead? Scholars have debated over that one for centuries! The whole story is to have spanned approximately 3 days, and can you really want to give your life for someone else after only 3 days? If that person was your own child, then certainly. But a lover? That's a judgement call - personally I have never been able to suspend my own belief regardingn that one, but some folks feel his actions make sense given the emotional nature of the character. He cannot imagine his life without Juliet - that is reasonable and believable. That he feels that way after only a few short days of knowing her is questionable in my book.
Hope this helps you formulate your own opinion on the subject!