Figure 2. A professor paces left and right while lecturing. Her position relative to Earth is given by x. The displacement of the professor relative to Earth is represented by an arrow pointing to the right. Figure 3. A passenger moves from his seat to the back of the plane. His location relative to the airplane is given by x.
Notice that the arrow representing his displacement is twice as long as the arrow representing the displacement of the professor she moves twice as far in Figure 3. Note that displacement has a direction as well as a magnitude. In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive usually that will be to the right or up, but you are free to select positive as being any direction.
Thus her displacement is. In this coordinate system, motion to the right is positive, whereas motion to the left is negative. His displacement is negative because his motion is toward the rear of the plane, or in the negative x direction in our coordinate system. Although displacement is described in terms of direction, distance is not.
Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them.
Distance traveled is the total length of the path traveled between two positions. Distance has no direction and, thus, no sign. For example, the distance the professor walks is 2. The distance the airplane passenger walks is 4. It is important to note that the distance traveled , however, can be greater than the magnitude of the displacement by magnitude, we mean just the size of the displacement without regard to its direction; that is, just a number with a unit. For example, the professor could pace back and forth many times, perhaps walking a distance of m during a lecture, yet still end up only 2.
It does not matter as long as the system is clear and consistent. Once you assign a positive direction and start solving a problem, you cannot change it. Figure 2. Given this information, is speed a scalar or a vector quantity? What has the student actually described? Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Is this temperature a vector or a scalar quantity?
Skip to main content. Search for:. Vectors, Scalars, and Coordinate Systems Learning Objectives By the end of this section, you will be able to: Define and distinguish between scalar and vector quantities.
Assign a coordinate system for a scenario involving one-dimensional motion. What is the difference between distance and displacement?
Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post.
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