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.