Distance and
displacement are two quantities that may seem to mean the same thing yet
have distinctly different definitions and meanings.
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 cancels the 4 meters west; and the 2 meters south cancels the 2 meters north. Vector quantities such as displacement are direction aware.
Scalar quantities such as distance are ignorant of direction. In
determining the overall distance traveled by the physics teachers, the
various directions of motion can be ignored.
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 click the button to see the answer.
- Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
- Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
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 click the button to see the answer.
The skier covers a distance of
What is the coach's resulting displacement and distance of travel? Click the button to see the answer.
(180 m + 140 m + 100 m) = 420 mand has a displacement of 140 m, rightward.
As a final
example, consider a football coach pacing back and forth along the
sidelines. The diagram below shows several of coach's positions at
various times. At each marked position, the coach makes a "U-turn" and
moves in the opposite direction. In other words, the coach moves from
position A to B to C to D.
What is the coach's resulting displacement and distance of travel? Click the button to see the answer.
The coach covers a distance of
(35 yds + 20 yds + 40 yds) = 95 yardsand has a displacement of 55 yards, left.
