Under your conditions, it's not necessary that the car make it all the way to 120 km/h. It depends on how long the car is going at slower speeds. If the car speeds up very quickly to a little over 100, in order to make up for the slow speeds, then theoretically, you wouldn't need to go as high as 120 km/h.

The real utility of the mean value theorem is in proving the Fundamental Theorem of the Calculus, which is by far the most important theorem in all of mathematics: it is responsible for the modern technological age.