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As an experiment, think of an object moving upward with a given
velocity. Suddenly it moves off with a velocity, say 45 degrees to the
vertical. If students are given this problem and asked what caused the
change in velocity, they generally reply that a force caused the change.
A more abstract reasoner might reply that an acceleration caused the
change in velocity, but this, I've found, is a very rare reply for a
student.
We do all of the prescribed experiments on displacement, velocity and
acceleration with the sonic ranger, but it is the twin concepts of
velocity and acceleration that cause students confusion. Actually, it is
really the concept of acceleration that is hard to understand and they
are constantly mixing it up with velocity. You don't believe this?
Observe students try to match their motion to an acceleration versus
time graph in the laboratory using the sonic ranger. It is obvious that
they are not clear what motion they have to make with their bodies to
create the acceleration vs. time graph that they see on the screen.
To a physicist, both acceleration and force are real observable
quantities, however, I think that of the two that acceleration is the
more abstract.