# Lesson Plan: Linear Motion with Integration Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use integration to get the average and instantaneous velocities and displacement vectors of a particle in straight-line motion.

#### Objectives

Students will be able to

- find the change in the velocity of a particle over a certain time period when given the acceleration function, ,
- find the velocity function of a particle, , when given the acceleration function , , and an initial condition:
- extend this to find the instantaneous velocity at a certain time,

- find the displacement of a particle over a certain time period when given the velocity function, ,
- find the displacement function, , when given the velocity function, , and an initial condition:
- extend this to find displacement at a certain time.

#### Prerequisites

Students should already be familiar with

- integration (definite and indefinite),
- vectors in 3D space,
- integrating vector-valued functions.

#### Exclusions

Students will not cover

- differentiation,
- acceleration as a function of position,
- nonlinear motion.