I'm 20 do you think I should be able to have my own moped?

I'm staying with my grandparents this summer as I have done since I was really young. My brother and I both have full time jobs in opposite directions and one car to share. I would like to buy a moped so that one person does not have to drive almost 2 hrs a day! My grandma says she is definitely against it and would be worried. Should I respect this? I don't want to worry my grandma but I think I am 20 and that I am old enough to be responsible for my own safety. What do you guys think I should do? There is no public transportation around.