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Analyzing Particle Movement: AP Calculus BC 2011 FRQ on Speed, Acceleration, and Distance

This resource explores Question 1 from the AP Calculus BC 2011 Free-Response Questions, focusing on the movement of a particle in the xy-plane. The question involves calculating the speed and acceleration of the particle at time ( t = 3 ), determining the slope of the tangent line to its path, and finding the total distance traveled over a specified interval. Instructions for using a graphing calculator to analyze the particle's movement are also provided, along with algebraic and numerical strategies for solution.

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Analyzing Particle Movement: AP Calculus BC 2011 FRQ on Speed, Acceleration, and Distance

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  1. Position, Speed, Acceleration, and Distance AP Calculus BC FRQ 2011 Question 1 By Samuel Fok

  2. Question: AP Calculus BC 2011 Form A #1 • At time t, a particle moving in the xy-plane is at position where and are not explicitly given. For and At , ,and

  3. Notes:

  4. (a) Find the speed of the particle at t=3, and find the acceleration vector of the particle at time t=3. • Algebraically and Numerically • What is the speed equation? Plug in Plug in

  5. (a) Find the speed of the particle at t=3, and find the acceleration vector of the particle at time t=3. • Algebraically, Numerically, and Calculator • Continue… 2nd 1st

  6. (a) Find the speed of the particle at t=3, and find the acceleration vector of the particle at time t=3. • Algebraically and Numerically • Continue…

  7. (a) Find the speed of the particle at t=3, and find the acceleration vector of the particle at time t=3. • Algebraically, Numerically, and Graphically • Continue… Acceleration

  8. (b) Find the slope of the line tangent to the path of the particle at time t=3. • Reminder:

  9. (c)Find the position of the particle at time t=3. X position at t = 3 is Y position at t = 3 is Position of Particle at time t = 3 is

  10. (d) Find the total distance traveled by the particle over the time interval • What is the distance formula?

  11. Graphing Calculator • Area=Total Distance Traveled • Step 1: Turn on your calculator • Step 2: Plug in equations • Step 3: Graph it

  12. Graphing Calculator • Area=Total Distance Traveled • Step 4: Press “Format” and then press “Zoom In” • Step 5: Press “2nd” and “Trace” • Step 6: Press the number 7 key

  13. Continue • Step 7: Enter lower and upper limit • Step 8: Press enter Distance Traveled approximately 21

  14. References • Collegeboard website • Math type • Microsoft Word • Microsoft PowerPoint • TI- 83+ Flash Debugger • Iphone Camera • Google.com • TI-84 Plus Silver Edition Calculator • Youtube • Youtube MP3 Converter

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