To find acceleration from a velocity-time graph, the formula used is a = (v(9.25) - v(9)) / (0.25 - 0), indicating uniform acceleration from 9:00 to 9:15. The distance traveled between 9 and 11 can be calculated using the integral of velocity, d = ∫9^11 v(t) dt, which represents the area under the curve. Different geometric shapes are considered to calculate this area, including triangles and rectangles, with specific dimensions leading to various distance values. The average velocity over the interval is calculated using the formula |v̄| = (1 / (11-9)) ∫9^11 v(t) dt. The discussion emphasizes understanding the relationship between velocity, area under the curve, and distance traveled.