OpenStax College Physics for AP® Courses, Chapter 2, Problem 4 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. This question is looking at path D in the figure here and we are asked to figure out what is the distance traveled and then figure out the magnitude of the displacement and displacement is different from distance in this question and then part (c) asks what is the displacement? So the distance is probably the quantity we are most familiar with in everyday life and this is the total amount of ground traveled you might say. So starting from here at a position of about 9 meters, we go all the way to this position of 3 meters and then turn around and go yet further another 2 meters from 3 to 5. So we have 9 minus 3, that's 6 meters initially, and then another 2 meters afterwards as you have to turn this corner for a total of 8 meters that's the distance traveled. The magnitude of the displacement and magnitude is illustrated with these absolute value signs these vertical bars which is to say, take this number as a positive whatever the number is, just make it positive we are interested only in the size of the number, not its sign. And the squiggly line on top or this, you know, arrow line on top is meant to say that this is a vector so we are taking the length of the vector, you might say, which is this displacement vector. In any case, what we are doing is finding the absolute value of the difference between the final position and the initial position and we are using the letter x because this is along the x-axis. So we have a final position of 5 meters and that's what this line is up to here, 5 meters, and then that's the final position and subtract from that the initial position which is 9 meters and then 5 minus 9 is negative 4 but we are taking the absolute value of that and so our answer is 4, that's the magnitude of the displacement, 4 meters. And then the displacement vector is the final position minus the initial position without these absolute value signs and so that's 5 meters—final position—minus 9 meters—initial position— giving us negative 4 meters and the negative sign indicates the direction of this displacement which is towards the left since to the right has been defined as positive that means negative is to the left. So negative 4 meters is the displacement.