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Lesson Plan: Maxima and Minima in Linear Motion Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to find the maximum and minimum values for the displacement and velocity of a particle moving in a straight line.

Objectives

Students will be able to

  • understand the physical constraints required for a model,
  • identify which intervals of a function are valid for the motion,
  • find the maxima and minima of the displacement and velocity of a particle,
  • find a different quantity (displacement, velocity, or acceleration) at the extrema.

Prerequisites

Students should already be familiar with

  • relating displacement, velocity, and acceleration using differentiation,
  • finding their instantaneous values.

Exclusions

Students will not cover

  • nonpolynomial functions,
  • motion that is not in a straight line,
  • higher-order time derivatives (higher than acceleration).

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