The big misconceptions about acceleration boil down to thinking that "acceleration" means the same thing as "velocity." Other than repetition and drill, I think the best way to bust the misconceptions is to make students write.
I might ask, "What is the direction of the car's acceleration? Justify your answer."
For years, I would accept for full or almost-full credit an answer like "The problem says the car is going west, but the car is slowing down. Slowing down means acceleration must move opposite the direction the car is going, so acceleration is east."
This year, I put my foot down. That answer earned zero or almost-zero credit, to my students' considerable protest and dismay:
"My answer's right," they said. "The acceleration is east."
Yes, but the justification is wrong.
"No it's not. You have a fact right here in the notes that says slowing down means acceleration and velocity move opposite each other."
That's emphatically NOT what I said. Acceleration does not "move." Acceleration "is." The correct justification says that "the acceleration IS opposite the direction of motion." When you say "acceleration moves east," you're implying that acceleration and motion are the same thing.
"Oh, come on, now. The car's moving, isn't it?"
Sure, but the direction of the motion is the direction of velocity. Acceleration does not have to be in the direction of motion.
"So you're going to take off all those points 'cause I got one word wrong?"
Conversation over -- I don't discuss points, only physics. The correct response here, student, is to pledge not to ever again refer to acceleration as "moving.\
Was it worth fighting with whiny freshmen who thought they knew physics better than I? Absolutely. We just finished three weeks of review for the cumulative final exam. Of all the mechanics topics we covered, motion was the one they handled best. Mistakes about the amount or direction of acceleration were rarer than ever.
The other major differences in my approach to kinematics this year was using units of "m/s per second" for acceleration rather than m/s2. I know that helped get students understanding what the magnitude of an acceleration meant. But I think the key to getting the direction right was fighting to eliminate the phrase "acceleration moves."
Isn't it also worth noting that velocity doesn't move either? The car moves, and the velocity expresses which way the car moves, but the velocity itself doesn't move. If you're going to put your foot down for acceleration, which I admire, shouldn't you put it down for velocity too? My ideal answer would be: "the car's velocity is directed eastward, but the car is slowing down, so the car's acceleration must be directed westward." Or almost as good, without 'velocity': "the car is moving eastward, but slowing down, so the car's acceleration is directed westward."
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