Mr. Integral
Math notes/Calculus III/Vectors and Geometry in Space

Space Curves, Velocity and Acceleration — Cheat sheet

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Core rule

v=r′,a=r′′,speed=∥r′∥,L=∫ab∥r′∥dt.v=r',\quad a=r'',\quad \text{speed}=\|r'\|,\quad L=\int_a^b\|r'\|dt.

Watch for

Constant speed can coexist with nonzero acceleration. A tangent line requires a nonzero velocity direction.