My maternal grandfather was a first-generation driver; he was well into his 20s when automobiles went into mass production. (I'm not sure when he first drove a car, but he could have driven in the last decade of the nineteenth century or first decade of the twentieth century.) That makes my mother a second-generation driver; me, a third-generation driver; and my children, fourth-generation drivers.
Coincidentally, my grandfather was a member of the first generation of his family to have been born here. (His ancestors were born in French Canada and France.) That makes my mother a second-generation American,* etc.
* By the second definition here.