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Lesson Overview: As youve already read, this is a self-contained module for calculus students. One-dimensional kinematics is typically covered in beginning calculus courses, whether the level is high-school honors, AP, or collegiate. This module could take 1-2 days depending on the readiness of the students and their allotted time. Ive included a guided worksheet for the students to complete as they go through the module. See the next page for copies of this, as well as the key.

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The module's primary emphasis is on the notions of rate of change, critical points, and a graphical understanding of the differences between position, velocity, and acceleration. Moreover, because this module was completed as a result of a research experience, Ive dedicated a portion of the site explaining how applied math connects with real-world phenomena, as well as other sciences. While this content isnt necessary for an understanding of the essential ideas, I believe that its important because students should be exposed to the nature of research in math and science! For more information regarding the nature of mathematics, I encourage you to check out the official benchmarks.

Essential Calculus Ideas: Show/Hide

  • Motion in one dimension (along any line) may be modeled on the Cartesian plane as time versus displacement from an origin.
  • Given a position function for an object, the slope of the function at a point (found by taking the derivative) gives the rate at which the particle is moving, or its velocity.
  • Speed is the absolute value of velocity.
  • Given a function for the velocity of an object, the slope of the function at a point (found by taking the derivative) gives the rate at which the velocity is changing, or its acceleration.
  • The critical points of a function for position or velocity indicate possible changes in the values (from positive to negative, or vice versa) of velocity or acceleration, respectively.
  • One may read the graph of a function for position or velocity to give information about velocity or acceleration.

NCDPI/AP Objectives: Show/Hide

  • 2.03, Interpret the derivative as a function: translate between verbal and algebraic descriptions of equations involving derivatives.
  • 2.05, Interpret the second derivative: identify the corresponding characteristics of the graphs of , ', and ".
  • 2.06, Apply the derivative in graphing and modeling contexts: interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

Offline Lessons: If you don't have access to the necessary technology, I've also included complete lesson-plans that form a unit on 1-D kinematics. Both lessons are designed for a 90-minute block schedule, and each includes a student note-sheet.

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