a particle moves along the x-axis so that its velocity at time t, for 0 ≤ t ≤ 6, is given by the differentiable function,

the velocity is zero at t=0 and t=3, and t=5 and the graph has horizontal tangents at t=1, and t=4

the area of the region bounded by the t-axis and the graph of x on the intervals [0,3], [3,5] & [5,6] are 8, 3, and 2. respectively. at time t=0, the particle is at x = -2

a. for 0≤ t≤ 6, find both the time and the position of the particle when the particle is further to the left. justify your answer.

b. for how many values of t, where 0 ≤t ≤6, is the particle at x = -8? explain.

c. on the interval 2 <t< 3, is the speed if the particle increasing or decreasing? give a reason for your answer

d.) during what time interval, if any, is the acceleration of the particle negative? justify your answer

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