I posted a rather straightforward question earlier that requires a good understanding of force, acceleration, and velocity in one-dimension. I asked readers of this blog to post a comment as to the answer to that mechanics question.
The answer is F, which means that all three scenarios are possible.
The question was taken from a physics education research paper with the above title, which you should be able to access for free. It has other questions on similar level that you might want to take a look. In fact, if you are an intro physics student, you might want to test your understanding by reading this paper and see how your understanding (or lack of it) is a serious topic of study.
Actually, if one understands the force, acceleration, and velocity at every part of the trajectory of a simple spring-mass system, one would see that the car-on-the-hill problem is no different.
Zz.
semantically speaking, I think it's possible that it is not moving (v=0), but it isn't possible that it is at rest (v=0 and a=0). My students often want to say things like a ball thrown straight upward stops or is "not moving" when it reaches the top of its trajectory. We try to explore the physical meaning of words like "stop", "not moving" and "at rest", which helps to see the value of just being able to specify the velocity and acceleration at the top and resolve any ambiguities from language.
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