Questions in this group present a graph and ask you to determine either the distance traveled or the displacement of the object. Pay attention to which quantity you're being asked to determine ... since it makes a BIG difference. In either case, you will need to use position coordinates to determine your answer. In the case of displacement, you will only need to determine the initial position coordinate (at t = 0.0 seconds) and the final position coordinate (at the end of the graph). In the case of distance, you will need to determine three position coordinates - the initial position, the position coordinate at the point when the object is a maximum distance from the starting position, and the final positioni coordinate. These coordinates allow you to determine the answer. The details that you need are in one of the two sections below. Read on!
Determining the Displacement
Displacement refers to how far out of place an object is at the end of the motion relative to the beginning of the motion. It is the overall change in position of the object. To determine the displacement, you will need to read the position coordinate for the starting position (t= 0.0 seconds) and for the final position (end of graph). Then find the change in these two positions. That involves subtraction.
Because displacement is a vector, it has a direction. Usually directions are adjectives like right or left or east or west. But graphs represent these adjectives with positive and negative values. So your answer could be positive or negative. Determining which sign to use is easy. Just subtract the initial position from the final position to get the change in position. (Incidentally, that's how you always calculate a change. ) If the result is negative, then enter a negative answer.
Displacement = Final Position - Initial Positio
Determining the Distance
Distance refers to how much ground is covered over the course of a motion. In this question, the object first moves in one direction away from the starting position. At a later time the person is a maximum distance from the starting position and then turns around and walks back towards the starting position. To determine the distance traveled from a position-time graph, you must be able to read coordinates off the graph. Using the coordinates, you must determine the distance from the starting position to the maximum distance away. Then use coordinates to determine the distance from the maximum distance away to the final position. Add these two values to determine the total distance.