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I am tutoring in physics, specifically in kinematics and uniform acceleration, and I thought it would be fun to find the time it would take for a car to drive around the globe given an initial velocity of $v_{0x}=4$ m/s, a constant acceleration of $10$ m/$s^2$. But then in order to find time we would need displacement, so I asked the student what would the displacement be (hoping for 40,075,017 m the earths circumference around the equator)? But one of the students said, "$0$m because we would end up back where we started." As far as I could tell she was correct, but that would lead us to the equation $$0m = (4 \text{m/s})t +5 m/s^2 t^2.$$ But this results in $t=0$ or $t=-.8s$ both of which are clearly incorrect.

My question is how would I reconcile this to a student? I am assuming that the issues come because I am applying equations that are restricted to one dimension to a 2-dimensional question.

How would one explain this discrepancy to a high-schooler?

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The high school kinematics problems normally assume one or two dimensional travel on a Euclidean plane. The earth is NOT a Euclidean plane, leading to the zero displacement issue. I suggest you reformulate this problem for your high school student such that you restrict the automobile to a flat two dimensional surface and have the automobile travel in a straight line for 40,000 km.

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  • $\begingroup$ Thanks. And yes that is what I did. $\endgroup$
    – Chris Christopherson
    Commented Nov 3, 2021 at 21:23
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    $\begingroup$ @ChrisChristopherson, you're welcomed, and I'm sure that you calculated a final velocity that was greater than earth's escape velocity. Also note that I taught high school physics for 13 years. If similar issues arise, I'll be happy to relate what I would do in any similar situations that I already witnessed in the class room. $\endgroup$
    – David White
    Commented Nov 3, 2021 at 23:13

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