Please check out this question excerpted from a standardized test for high-school students in a North American country;
It says: Which of the following would be a graph of speed vs. time for the car on this track?
The problem is that this question seems reasonably clear and straight forward. The car speeds up and then slows down. How difficult could that be? But it’s in those tiny details that things get complicated. Does the car start from rest? Is it already moving? Does the car have a motor? Could the car even make it to the top?
Both the plots would be wrong without a significant start impulse or initial speed, because otherwise the car would not be able to finish the loop and would either return backwards or fall while climbing. Therefore, a sufficient impulse must be provided, and this seems to rule off plot ‘B’, if we accept, rather reasonably, that the origin of the speed axis is zero. But, of course, the speed would increase further with the first descending part of the track, while plot 'A' claims the opposite. Coming to this point, the student may come to the conclusion that the beginning part of plot ‘A’ might hold if the toy car has brakes, to soon realise that the car should also have motor if plot ‘A’ is correct. All this stuff (motor and brakes) does not seem to make much sense, since gravity is supposed to drive the car all the way. Of course, with a motor, the initial impulse would be no longer needed, and plot 'B' could be granted a second look. Unfortunately, the final trend is the same at both the track and plot 'B', while the opposite was to be expected. So, even if the student reluctantly accepts the motor trick just for the start, plot ‘B’ would still fail by its end. At this point, the student may (hopefully) realise that he can actually choose any plot, by accepting that mutual exclusion holds, meaning that if one plot clearly does not holds, the other could be considered ‘correct’, at least in this restrict sense. So, he can finally expect to answer 'right', by picking one plot by chance, unless, of course, it is authoritatively decided that he should not have selected any plot, because both the plots are unable to translate correctly the whole movement.
This lecture video, on the physics of a roller coaster loop, helps to understand that for starting the initial drop with zero speed, the initial height must be significantly higher than depicted at the above drawing.
https://www.youtube.com/watch?v=zcwyf_CE6mM
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