another road up a mountain

A road up a parabolic mountain is being planned. Can you devise a measure of "steepness" for the road? Does your measure depend on where you are on the road? Can you devise a measure of "curvy-ness" for the road? Does your measure depend on where you are on the road? Compare this applet with the "road up a mountain" applet on this website? How are the two applets similar? How do they differ? What questions could / would you put to your students based on this applet ?