Distance and displacement are two quantities which may
seem to mean the same thing, yet they have distinctly
different meanings and definitions.
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.
Example
To test your
understanding of this distinction, consider the
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 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.
Exercise 1
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 distance traveled by the
skier and the resulting displacement during these three minutes.
Then depress the mouse
on the pop-up menu below to see the answer.
Exercise 2
Seymour Butz
views football games from under the bleachers. He
frequently paces back and forth to get the best view.
The diagram below shows several of Seymour's positions at
various times. At each marked position, Seymour makes a
"U-turn" and moves in the opposite direction. In other
words, Seymour moves from position A to B to C to D. What
is Seymour's resulting displacement and distance of
travel? Depress the mouse on the pop-up menu below to see
the answer.
To understand the distinction between
distance and displacement, you must know their definitions
and you must also know that a vector
quantity such as displacement is
direction-aware whereas 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 in the opposite direction effectively
begins to cancel whatever displacement there once
was.
Check
Your Understanding
1. What is the displacement of the GBS cross-country
team if they begin at the school, run 10 miles and finish
back at the school?
2. What is the distance and the displacement of the
race car drivers in the Indy 500?
