Lesson Plan: Applications of Derivatives on Rectilinear Motion | Nagwa Lesson Plan: Applications of Derivatives on Rectilinear Motion | Nagwa

Lesson Plan: Applications of Derivatives on Rectilinear Motion Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to apply derivatives to problems of motion in a straight line.

Objectives

Students will be able to

  • find the absolute extrema (maximum and minimum values) for displacement and velocity,
  • find the intervals over which a body has positive or negative velocity (increasing or decreasing displacement),
  • find the intervals over which a body has positive or negative acceleration (increasing or decreasing velocity),
  • find the instantaneous value(s) of displacement, velocity, or acceleration for a given value of one of the other quantities (displacement, velocity, or acceleration),
  • find the acceleration when velocity is given as a function of position (using the chain rule),
  • find the average speed over an interval when given displacement (specifically instances where the particle changes direction within the given time interval).

Prerequisites

Students should already be familiar with

  • differentiation,
  • the chain rule,
  • the first and second derivative tests.

Exclusions

Students will not cover

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

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