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Name: ---------- AP Calculus AB Worksheet - Rectilinear and Projectile Motion 1) A particle is moving along a straight path with it's position defined by 2 set) = 2t 3 + 3t - 36t + 40 where t is in seconds and s is in feet. a) What are the particle's velocity and acceleration functions? b) What is the total distance traveled by the aprticle In the first three seconds? c) What is the displacement of the particle after the first eight seconds? 2) A silver dollar is dropped from a building that is 1,362 feet in height. Time is in seconds. a) What are the silver dollar's height, velocity and acceleration functions? b) When does the silver dollar hit the ground and what is its impact velocity? c) How far does the silver dollar travel between t=1 and t=2 seconds? 3) The displacement in feet of a body moving along a line at any time t in seconds is given by s(t) = t 3 - 6t 2 + 9t + 5. a) What are the velocity and acceleration functions? b) Find the total distance traveled from t=O seconds to t=4 seconds. c) What is the velocity of the body when the position is 8 feet? d) Sketch a motion schematic. Be sure to label the time, position, and velocity at each change in direction and at the beginning. c:\~\J~" 4) A marble is thrown straight q from the top of a 220-foot building. Its initial velocity was 22 ft. per second. a) What are the marble's height, velocity, and acceleration functions? b) When does the marble hit the ground and what is its impact velocity? c) What are the velocity and position at three seconds? d) What is its velocity after falling 108 ft? 5) A particle is traveling on a straight path and its position is defined by set) = t 3 - 9t 2 + 24t + 20 feet in t seconds. a) What are the velocity and acceleration functions? b) What is the total distance traveled by the particle during the first eight seconds? c) What is the displacement of the object after the first eight seconds? 6) A bag of sugar is launched vertically upward from a height of 455 feet with an initial velocity of 102 feet per second. a) What are the bag's height, velocity, and acceleration functions? b) What is the position of the bag when the velocity is 22 feet per second? c) When will the bag hit the ground? What is its impact velocity/ d) When will the bag reach its maximum height? What is its maximum height? e) What is the velocity of the bag when it is 250 feet above the ground?

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Course Name, AP Calculus, Course Description, Advanced Placement, Calculus AB, AP Calculus BC, AP Calculus AB, Student Handbook, the College Board, High School

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posted: | 6/11/2011 |

language: | English |

pages: | 3 |

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