Hubisz replies: “Acceleration” is a very difficult concept. It is a second-order effect: a rate of change with respect to time of a rate of change with respect to time. It may well be that it is too much for middle-school students, but, regardless, it is mentioned in most physical sciences texts; the definition should be correct, even if the only objective is to have the students memorize something.
Galileo reviewed previous attempts at describing accelerated motion, rejected them, and considered both the rate of change of speed (not velocity) with respect to distance and the rate of change of speed with respect to time. 1 He rejected the former, for reasons that were not too clear, but accepted the latter on the guess that it fit his work on freely falling bodies. This leap of Galileo’s is very sophisticated and certainly not “dictated by logic.” Logic can only assure us that the process is correct; it says nothing about the physics that Galileo insisted his definition satisfy.
What can we do? Follow Galileo. Forget putting the definition in the textbooks. Have the students carry out experiments. Encourage them to investigate the phenomenon first before we throw definitions at them. They will learn that velocity is not always constant, that the problem is not trivial, and that they have a lot more to learn, perhaps in high school, maybe in college.
