Question

a partial moves along the x-axis so that its velocity at time t, for 0< = t = < 6, is given by a differentiable function v whose graph is shown above. The velocity is 0 at t=0, t=5, and the graph has horizontal tangents at 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= -2.

a) for 0 < = t < = 6, find both the time and the position of the particle when the particle is farther to the left.

b) for how many values of t where 0 < = t < = 6 is particle at x= -8?

c) on the interval 2<t<3 is the speed of the particle increasing or decreasing?

d) During what time intervals if any is the acceleration of the particle negative?