A particle moves along the $x$-axis so that its velocity at time $t$, for $0 \leq t \leq 6$, is given by a differentiable function $v$ whose graph is shown above. The velocity is 0 at $t = 0 , t = 3$, and $t = 5$, and the graph has horizontal tangents at $t = 1$ and $t = 4$. The areas of the regions bounded by the $t$-axis and the graph of $v$ on the intervals $[ 0,3 ] , [ 3,5 ]$, and $[ 5,6 ]$ are 8, 3, and 2, respectively. At time $t = 0$, the particle is at $x = - 2$.
(a) For $0 \leq t \leq 6$, find both the time and the position of the particle when the particle is farthest to the left. Justify your answer.
(b) For how many values of $t$, where $0 \leq t \leq 6$, is the particle at $x = - 8$ ? Explain your reasoning.
(c) On the interval $2 < t < 3$, is the speed of the particle increasing or decreasing? Give a reason for your answer.
(d) During what time intervals, if any, is the acceleration of the particle negative? Justify your answer.