Parametric Functions and Motion Analysis

Mr. Bean introduces parametric functions, focusing on their components and direction of motion. He explains how to determine if a particle is moving left, right, up, or down by analyzing the x and y components. The lesson includes an example using a circle and discusses how to change the direction of motion by altering the parameter. Finally, Mr. Bean covers the rate of change, explaining how to calculate the slope between two points on a parametric curve.

What are the components of a parametric function?

• Forward and backward components

• Up and down components

• Left and right components

• Horizontal and vertical components

How can you determine if a parametric function is moving left or right?

• By checking if both X and Y of T are decreasing

• By checking if both X and Y of T are increasing

• By checking if X of T is increasing or decreasing

• By checking if Y of T is increasing or decreasing

What happens to the direction of motion as time increases in a parametric function?

• It always moves right

• It always moves left

• It can change

• It remains constant

What is the parametric equation for a circle given in the example?

• F of T equals sine T

• F of T equals cosine T

• F of T equals cosine sine T

• F of T equals sine cosine T

What assumption is made about direction changes in parametric functions?

• Direction never changes

• Direction changes only at specific values of T

• Direction changes randomly

• Direction changes continuously

How do you determine if a particle is moving up or down?

• By checking if X of T is increasing or decreasing

• By checking if both X and Y of T are decreasing

• By checking if both X and Y of T are increasing

• By checking if Y of T is increasing or decreasing

What does the graphical representation of parametric functions show?

• The exact path of the particle

• The direction of motion

• The rate of change

• The components of the function

How can you write a parametric function differently?

• By changing the equation

• By changing the direction

• By changing the parameter

• By changing the components

How do you change the direction of motion in a parametric function?

• By keeping the parameter constant

• By negating the parameter

• By increasing the parameter

• By decreasing the parameter

What is the result of changing the direction using negative parameters?

• The graph changes shape

• The graph becomes a straight line

• The graph remains the same but direction changes

• The graph disappears