AP+Review+4+Question+2

A particle moves along the x-axis so that its velocity at time t is given by v(t)= -(t+1)sin((t^2)/2). 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 time t=0 until the time t=3. d) During the closed interval [0,3], what is the greatest distance between the particle and the origin? Show the work that leads to your answer.

- Chloe Rose Nielsen


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