Displacement and distance traveled calculus
[DOC File]Section 1
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Use integrals to solve distance problems to find the displacement or total distance traveled. Vocabulary: Indefinite Integral – is a function or a family of functions. Distance – the total distance traveled by an object between two points in time. Displacement – the net change in position between two points in time . Key Concept:
[DOC File]AP Calculus AB
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3. The displacement in feet of a body of water moving along a line at any time t in seconds is given by . What are the velocity and acceleration functions? Find the total distance traveled from t = 0 seconds to t = 4 seconds. What is the velocity of the body when the position is 8 feet? Sketch a motion schematic.
[DOC File]AP Calculus AB
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Find the displacement and the total distance traveled by the particle from t = 1.5 seconds to t = 7 seconds. 5. A person is standing on top of the Tower of Pisa and throws a ball directly upward with an initial velocity of 96 feet per second. The Tower of Pisa is 176 feet high.
[DOC File]AP Calculus
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a) What is the particle’s displacement? b) What is the total distance traveled? 6. The rate of consumption of oil in the U.S. during the 1980s (in billions of barrels/year) is modeled by the function, where t is the number of years after January 1, 1980. Find the total consumption of oil in the U.S. from January 1, 1980 to January 1, 1990.
[DOC File]Motion Notes for calculus
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Displacement is the _____ in positions between two times. Can displacement be negative?_____ Total distance traveled by a particle is the sum of the amounts it displaces between the start and all stop(s) and the end. Can distance be negative? _____ Motion practice Name: AP Calculus
AP CALCULUS
Displacement (change in position) from is Displacement = Total Distance traveled from is Total Distance = or Total Distance = , where changes sign at _____ CALCULUS BC ONLY. Differential equation for logistic growth: Integration by parts: Length of arc for functions: _____
[DOC File]AP Calculus
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The displacement of the particle during the given time interval. The distance traveled by the particle during the given time interval., 0 < t < 3, 1 < t < 6. The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. Find: The velocity at time t. The distance traveled during the given time interval.
[DOC File]AP Calculus AB
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e) What is the displacement and total distance traveled for the indicated interval specific to each problem? f) When is the particle speeding up? Slowing down? g) Find the velocity when the acceleration is 0. 1. s(t) = t3 –3t + 3 displacement and total distance traveled in [0, 6] 2.
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