Precalculus: Particle Motion 2

Objectives

• Students will analyze the relationship between the motion of a particle along a straight line and the behavior of the graph of a general position function.
• Students will compare the steepness and direction of a position function to the velocity function.
• Students will visualize total area and signed area and relate these calculations to cumulative distance and position.

Vocabulary

• position
• velocity
• magnitude
• cumulative distance
• signed area
• total area

About the Lesson

This lesson involves the motion of a particle along a straight, horizontal line associated with a general position function.
As a result students will:

• Analyze the behavior of the graph of the position function as the particle moves to the left, right, and changes direction.
• Compare the steepness of the graph of the position function to the velocity of the particle.
• Compare and contrast total area and signed area, and relate these calculations to cumulative distance and position.
• Use the graph of the position function to describe the general motion of a particle.
• Create position functions which satisfy given conditions.