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Apply FTOC

Apply FTOC. Recall velocity Acceleration = rate that velocity changes How do we get from acceleration back to velocity?. Example. A particle moves along a line so that its velocity at time t is (meters per second). Find the displacement of the particle during the time period .

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Apply FTOC

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  1. Apply FTOC • Recall velocity • Acceleration = rate that velocity changes • How do we get from acceleration back to velocity?

  2. Example A particle moves along a line so that its velocity at time t is (meters per second). • Find the displacement of the particle during the time period . displacement = change in position m The particle moved m to the left.

  3. Example A particle moves along a line so that its velocity at time t is (meters per second). • Find the distance traveled during the time period . • Find when the particle changes direction. • Find the distance for each piece of the interval and add them together. m

  4. Example Find the velocity equation and position equation of a particle if its initial velocity is 20 ft/s and its initial position is 200 ft above the ground. • Acceleration of gravity =

  5. In general, Homework: p. 293 #69-72, 75

  6. p. 293 #69-72, 75 70. a) m b) m 69. a) m b) m

  7. p. 293 #69-72, 75 72. m 71. on [0, 10] m

  8. p. 293 #69-72, 75 75. Find width and height – area of rectangles (10-second intervals) Interval  [0, 100], use 5 subintervals sec Velocity given in mph  20 sec = mi

  9. Test Review General antiderivatives FTOC Position, Velocity, Acceleration • Given , find the velocity function. Find after 2 seconds. • Given on [1, 5] a) Find displacement. b) Find the total distance traveled. • If an object is dropped from a 300-foot building, what will be its position after 4 seconds?

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