I agree with Su; I suppose you can relax while you take a ride haha. There are so many intonations you can use with "go for a ride" that will bring about many different meanings. It is possible to tell someone: "Hey, you look worried, let's go for a ride and talk about it," and have it mean "Let's ride around to refresh ourselves and talk about things." In many cases it's quite literal, the person will actually be driving somewhere....

I've never heard it with that meaning. It probably just means what it says - take a short trip for pleasure. Go for a ride in car, on a bike....

I understand that you can relax while you "go for a ride", but it not the same. It means that you go for a walk.

"go for a ride" does not also mean to relax for a while. It could mean that you are taking a break from another activity. I want to stop studying for a while so I'll go for a ride. To relax means to do very little, such as napping or watching television.