Signature Assignment

Math 1100 Signature Assignment: Derivatives Suppose that a particle moves according to the law of motion 𝑠𝑠(𝑡𝑡) = 𝑡𝑡4 − 6𝑡𝑡3 + 4𝑡𝑡2 + 3 with t ≥ 0, where s is in meters and t is in seconds. Use your knowledge of the relationship between position, velocity, and acceleration to answer the following questions. Use exact values (not approximations) throughout. a) Find the velocity of the particle at time t. What is the velocity at t = 0?

b) Determine, using algebraic analysis, when the particle is moving in a positive direction, a negative direction, and when it is at rest.

c) Find the total distance traveled by the particle in the first 6 seconds.

d) Find the acceleration of the particle at time t. What is the acceleration at t = 0?

e) When is the particle speeding up and slowing down? Explain how you found your answers.

Show all your steps and include narrative text explaining your work to your reader.

Include computer generated graphs of your position, velocity, and acceleration functions. Explain how the graphs support your answers to parts a – e above. Note that the graph is not providing the answers, but supporting the mathematical steps and calculations you made before using technology to graph the functions. Merely pointing to a graph to explain any of your answers above is not an acceptable method of demonstrating understanding.

Write a paragraph reflecting on your solution process. What problems did you encounter in completing the assignment? How did you troubleshoot them, if you did? What new skills or insights did completing the assignment give you? Give a specific “real world” example of the use of derivatives that is significantly different from the problem you just solved. Your example should include the meaning or purpose of the derivative and an explanation of why it may be important in a real application. Cite any sources used.

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Expectations:

All signature assignments must be completely word processed, including using an equation editor for all mathematics. Hand-written work will not be graded. All mathematical steps must be shown and there must be narrative in place to explain your process to your reader. Any charts or graphs will also be computer generated. Your problem will be presented in a clear and logical way. A signature assignment should be an exposition of your finest work and presentation.

There are writing labs on campus for general writing help. For help using the equation editor in Microsoft Word go to https://www.youtube.com/watch?v=Cir8RXGTEq8