OpenStax College Physics for AP® Courses, Chapter 2, Problem 2 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. There are two answers to this question that are almost equally correct and we'll find a small distinction that's gonna make us choose (b) over (d). But first of all, let's consider what's happening here; we have a feather being dropped and the student wants to measure a positive velocity and a positive acceleration. So that means that the downward direction has to be positive because the feather's going to be moving down and in order to consider that velocity positive, we need the downward to be the positive direction and furthermore, the acceleration is downwards since that's the direction of the net force due to gravity and so likewise, downward makes that acceleration positive too. So down has to be positive and that's really the only thing that's necessary in order to have positive velocity and positive acceleration and so both answers (b) and (d) satisfy that criterion that downward is positive. So this downward direction should be positive and downward direction should be positive. So how do we choose between these two? Well, if she also wants the position of the feather to be positive then that would make (b) the better answer and the question doesn't really say that she wants that but we need to find some way to distinguish between (b) and (d) and so let's assume that she might also want that. She seems to want the velocity and acceleration to be positive maybe the position should be positive as well. So if her hand, which is here, is taken to be the zero point— that's a position of y equals zero meters— then that means as the feather falls below that point, downward being the positive direction, we are going to have a positive displacement so this will be y equal maybe to 2 meters; it's fallen 2 meters down given that this is zero, this would be 2. If we had the floor as the reference level, zero, and down as positive that would mean below the floor would be some positive number like say y equals 1 meter and above the floor would be a negative number say y equals negative 1 meters. So if you want a positive position for the feather then you want to have your coordinate system begin above the initial position of the feather so that it's going to have a positive position as it goes down given this unconventional choice of down being positive.