Graphing Position Velocity and Acceleration

Graphing Position Velocity and Acceleration

Graphing Position, Velocity, and Acceleration

For this Critical Thinking Assignment, you will be using GeoGebra to sketch graphs and solve real-world examples.

Begin by reading the following scenario:

After a diver jumps off a diving board, the edge of the board oscillates with position given by s(t) = −5cos(t) cm at t seconds after the jump.

Part I: Complete the following steps:

1. Using the GeoGebra tool (https://www.geogebra.org/graphing?lang=en), sketch one period of the position function for t ≥ 0.
2. Find the velocity function.
3. Using the GeoGebra tool (https://www.geogebra.org/graphing?lang=en), sketch one period of the velocity function for t ≥ 0.
4. Determine the times in the first period (or a single period) when the velocity is 0.
5. Find the acceleration function.
6. Using the GeoGebra tool (https://www.geogebra.org/graphing?lang=en), sketch one period of the acceleration function for t ≥ 0.
7. Save your GeoGebra work as a .pdf file for submission.

Part II: Based on your work in Part I, discuss the following:

1. Discuss any observations you can make about the relationships between the graphs of the position, velocity, and acceleration functions. In particular, make sure to include the following:
   1. The connections between critical points on each graph.
   2. The similarities and differences among the characteristics of the three graphs (i.e. amplitude, midline, and period).
   3. How fast is the edge of the board moving after 2 seconds?
   4. Based on your graph, over what intervals is the edge of the diving board moving upward?
2. Discuss how your answers to Part I would be affected if:
   1. The sign of the coefficient of cos(t) were opposite.
   2. The coefficient of cos(t) were double.
3. Provide at least two other real-world situations that serve as applications to this concept and respond to the following:
   1. What common characteristics do the real-world scenarios you chose share?
   2. What did you look for in the way that the real-world scenario can be modeled?

Requirements:

You must submit two files for this assignment.

1. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.
2. The second file should be a narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:
   1. Your paper should be 2–3 pages in length (not counting the required title page and references page).
   2.  Cite and integrate at least two credible outside sources.
   3. Include a title page, introduction, body, conclusion, and a reference page.
      1. The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
      2. The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
      3. The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
   4. Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required paper length excludes any tables, graphs, etc.)