Taylor series derivation of x(t) for 1-D motion with constant acceleration скачать в хорошем качестве

Taylor series derivation of x(t) for 1-D motion with constant acceleration

The position as a function of time for 1-D motion with constant acceleration is derived by expanding x(t) in a Taylor Series. This video is reference [2] in: Craig W. Looney, "Taylor Series Kinematics," The Physics Teacher 63 , 349–351 (May 2025). https://doi.org/10.1119/5.0173909. [Preprint available at https://arxiv.org/abs/2506.06170. Video abstract available at    • Taylor Series Kinematics Video Abstract  .] *** NOTATION: normally, I prefer to put an "x" subscript on the symbols for 1-D motion quantities such as velocity and acceleration (assuming I am using "x" for the 1-D position) in order to emphasize that these are signed quantities that represent vector components (not to be confused with always-positive magnitudes) and also to use multi-dimensional-compatible notation from the outset. HOWEVER, in this video I have left off the "x" subscripts in order to simplify the notation and make it easier to follow the details of the derivation. *** THANK YOU: I thank Dr. Dan Tambasco (emeritus, Merrimack College) for pointing out to me many years ago that the basic 1-D constant acceleration kinematic equations are Taylor Series expansions.