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.
