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Lesson Plan: Linear Motion with Derivatives Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use differentiation to find the instantaneous velocity, speed, and acceleration of a particle.

Objectives

Students will be able to

  • find the speed of a body, |𝑣(𝑡)|, when given the distance traveled as a function of time and extend this to find the instantaneous speed at a certain time,
  • find the velocity of a body, 𝑣(𝑡), when given displacement or position as function of time and extend this to find the instantaneous velocity at a certain time,
  • find the acceleration of a body, 𝑎(𝑡), when given velocity, displacement, or position as a function of time and extend this to find the instantaneous acceleration at a certain time.

Prerequisites

Students should already be familiar with

  • differentiation of power, trigonometric, exponential, and radical functions,
  • differentiation of piecewise functions,
  • vectors in 3D space,
  • speed as the magnitude of velocity.

Exclusions

Students will not cover

  • integration,
  • velocity or acceleration as a function of position,
  • nonlinear motion.

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