4. A particle 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 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 t 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 t 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.
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 t 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 t 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.