Between the Lines.

♥ Sunday, June 17, 2007 1:04 AM

Distance and Displacement

Distance and displacement are two quantities which may seem to mean the same thing, yet have distinctly different definitions and meanings.

Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.
Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

To test your understanding of this distinction, consider the following motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m). Yet when she is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention and regard to direction. The 4 meters east is canceled by the 4 meters west; and the 2 meters south is canceled by the 2 meters north.

Now consider another example. The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes. Then depress the mouse on the pop-up menu below to see the answer.

answer: The skier covers a distance of

(180 m + 140 m + 100 m) = 420 m

and has a displacement of 140 m, rightward

To understand the distinction between distance and displacement, you must know the definitions and also know that a vector quantity such as displacement is direction-aware and a scalar quantity such as distance is ignorant of direction. When an object changes its direction of motion, displacement takes this direction change into account; heading the opposite direction effectively begins to cancel whatever displacement there once was.