Is there no correct answer on this question?

Question

Again, this is the link to the Imgur post I made to get the photo online: https://i.stack.imgur.com/vq8qH.jpg This was a question on an exam I recently conducted, and the results said that option "A" was the correct answer, however it doesn't look like "A" has any curve, whereas when I graphed it after the test there seemed to be a graph. My teacher said that the first few dots may not be used due to inaccuracy, but the graph should still be different. What is the answer to this question (if there is one), because I'm trying to see if I would be able to gain extra marks? Thank you so much, this means a lot to me.

Answer 1

None of the answers are right. Let's take the right direction to be the direction of positive displacement (which is a reasonable assumption, because that's usually the assumption for such multiple choice questions).

Based on the very limited information given, I'll assume the simplest possible setup; namely that the object keeps moving to the right. As a result, the displacement $s$ needs to be an increasing function of $t$. This immediately eliminates $B,C,D$. Finally, $A$ is wrong because it depicts a constant slope, which means the velocity is constant; this is incorrect, because if the velocity really was constant, then the dots would be evenly spaced apart (because the dots are taken equal time intervals apart).

The correct graph (under the assumptions stated above) should look something like an $\arcsin(x)$ graph or a $\sinh(x)$ graph. The slope should initially be positive and high in magnitude (i.e it is moving a large distance in a given time interval), then somewhere in the middle, it should still be positive, but slightly lower in magnitude (it travels smaller distance in same time interval), then at the end the slope should be positive and high in magnitude again (it moves a large distance in the same time interval).

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Also, the reason given by your teacher that "first few dots may not be used due to inaccuracy" makes no sense. First of all, there is no such information given in the question to suggest that this is an experiment performed by a student or any other contextual clues to suggest that the first few data points should be ignored. So, the most reasonable assumption (in the given situation of a multiple choice question on what looks to be a high-school level exam) one can make for the question is to assume that the given information is perfect, without any sort of experimental error.