A particle moves along the x-axis so that its velocity at time t, for 0 6, ≤ ≤t 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 0, ] t = the particle is at 2.(b) For how many values of t, where 0 6, ≤ ≤t is the particle at 8 ? x = − Explain your reasoning

Question

A particle moves along the x-axis so that its velocity at time  t, for  0 6, ≤ ≤t 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 0, ] t = the particle is at 2.(b)  For how many values of  t, where  0 6, ≤ ≤t is the particle at 8 ? x = − Explain your reasoning