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

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

c. On the interval 2

d. During what time interval, if any, is the acceleration of the particle negative?