i.imgur. com/cqwun. png
i'm kind of stuck.. are the answers 6, -3, -3, and 0?
6 is the correct 1st answer.
looking at the graph,
a(t) = 3 - 3/2 (t-2) for t>=2
so,
v(t) = 6t - 3/4 t^2
v(2) = 6*2 - 3/4 * 4 = 9
v(4) = 6*4 - 3/4 * 16 = 12
so, ∆v = 3
Note that even though a is decreasing, it is still positive, so v will be increasing
v(6) = 6*6 - 3/4 * 36 = 9
so, ∆v = -3
from t=0 to 6, v went +6 +3 -3 = +6