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As usually stated:

Newton’s first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.

I want to know, what do we mean by "straight line" in this law? Since this law was first presented in a classical flat spacetime without any torsion, could we distinguish between motion in straight line or motion on the autoparallel curve in that limit?

The answer could be useful to describe the trajectory of the free falling particle in the Einstein-Cartan manifold.

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