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A particle moves along the x -axis so that its velocity at time t is given by At time t = 0, the particle is at position x = 1 (a) Find the acceleration of the particle at time t = 2. Is the speed of the particle increasing at t = 2? Why or why not? (b) Find all times t in the open interval 0 < t < 3, when the particle changes direction. Justify your answer. (c) Find the total distance traveled by the particle from t = 0 until time t = 3. (d) During the time interval0 t 3, what is the greatest distance between the particle and the origin? Show the work that leads to your answer.

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(a) Find the acceleration of the particle at time t = 2. Is the speed of the particle increasing at t = 2? Why or why not?

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(b) Find all times t in the open interval 0 < t < 3, when the particle changes direction. Justify your answer.

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(c) Find the total distance traveled by the particle from t = 0 until time t = 3.

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(d) During the time interval0 t 3, what is the greatest distance between the particle and the origin? Show the work that leads to your answer.

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Work Cited "AP Calculus AB 2003 Scoring Guidelines." Apcentral.collegeboard.com. College Entrance Examination Board. Web. 26 May 2011..

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