Time Translation and the Taylor Structure of Kinematics
Abstract
Recent discussions have emphasized the use of Taylor series to explain the familiar kinematic relations in the introductory calculus sequence. In this note we show that the connection can also be made in the opposite direction. By examining how the familiar kinematic relations behave under translation in time, the series structure appears naturally within elementary kinematics. In this way, extensions of motion such as jerk become accessible at the pre-calculus level, while also providing students with a natural motivation for the Taylor series encountered later in calculus.
Reference
Time Translation and the Taylor Structure of Kinematics, The Physics Teacher.
Status: Accepted for publication; forthcoming.
Volume, page numbers, and DOI will be added when assigned.
Quick course
A short companion PDF introducing the time-translation derivation.