Mail time: airplane and car with the same acceleration, which moves faster?

A summer institute participant asks: 

I had a quick physics question from one of your daily quizzes: Which is moving faster, a car with an acceleration of 2 m/s/s, or an airplane with an acceleration of 2 m/s/s? My answer was airplane but my students are not happy with that answer. Is there any way you could explain it to me so I make sure I am telling them the correct answer?

Awesome, important question - this is a "holy grail" question for understanding motion.  

Acceleration tells the CHANGE in speed every second.  Both the car and the airplane gain 2 m/s of speed each second.  

But this doesn't say how fast either moves!  Sure, if the airplane is cruising and speeds up a bit, while the car is entering the freeway, the airplane moves faster.  But, say the airplane is starting from rest on the runway, and speeds up to 2 m/s after one second, 4 m/s after two seconds, etc.  Then say the car is on the freeway.  The car is initially moving 30 m/s, then 32 m/s, then 34 m/s, etc.  The car is moving faster - yet the objects have the same acceleration!

Hope this helps.  The answer is, WE DON'T KNOW.

GCJ