This question is about a discrepency between the method of finding average velocity via "change in distance over change in time" and the other method of "instantaneous velocity + instantaneous velocity all divided by 2" If I find average velocity of various points on a position vs position graph, then find instanenous velocity of each of those points, if I then recalculate average velocity based on the instantaneous velocities (as opposed to finding magnitude of average velocity based on the information provided in the position vs position graph), how come the average velocities of one method don't match up with the average velocities found using the other method? For instance, why do I get 18.9 when finding average velocity when I feel like I should be getting 17.2 as I did when I calculated average velocity in the beginning? What is accounting for the difference? Am I making an incorrect calculation, or is my calculator creating a discrepancy? Is the shorthand process of finding the derivative equations (as opposed to using the formal definition of derivative) for x(t) and y(t) not exact enough? So my question is, why am I getting 18.9m/s and not 17.2m/s? Here's an illustration of my question: EDIT: I removed the embeded illustration. Both question and answer are still clear without illustration.