The velocity of a particle can be modeled by the function mc041-1.jpg. which graph accurately shows the velocity of the particle at any time, t?

The simplest way to solve this is to notice that letting t = 8/3 will let the term (3t-8) = 0. Substituting this will make v(t) = 2. Then we check which graphs pass through (8/3, 2). Only the second and third graphs do.

Next, we look at the behavior of the graph as t increases. Based on the equation, as t increases, (3t-8)^3 increases as well, so v(t) will increase as well. This is shown by the second graph, in which v(t) increases as t increases.