2.1. Locating an Object: Distance and Displacement http://www.ck12.org
Displacementis the difference between final and initial positions.
∆x=Pf−Pi, wherePfis the final position of the object andPiis the initial position of the object.
Determining Distance and Displacement
Place a dot anywhere along a line and you have identified a position for an object. Let’s imagine a marble on the line
at position, P1 = 3 units, that travels to position P2 = 7 units, and then turns around, ending its journey at the origin
P3 = 0 units (illustrated inFigure2.3).
FIGURE 2.3
A marble rolls from P1 to P2 and back to
P3.- What distance has the marble traveled from P1 to P3?
- What is the displacement of the marble from P1 to P3?
To answer the first question, we add the distance the marble moved from P1 to P2 and then from P2 to P3 without
regard for direction.
|P1 - P2| = 4 units
|P2 - P3| = 7 units
|P1 - P2| + |P2 - P3| = 11 units
To answer the second question we note where the marble started (3 units) and where the marble ended (0 units).
P1 = 3 units
P3 = 0 units
P3 - P1 = 0 - 3 units = -3 units
The displacement of the marble is therefore three units to the left. Notice that the first case (distance) gives no
information on the final position of the marble, and the second case (displacement) gives no information about the
total distance the marble travels.
The use of negative signs in physics typically indicates direction, rather than quantity. A position of -3 units is not a
larger position than -5 units, even though mathematically, negative three is larger than negative five.
Using Graphs to Distinguish Between Distance and Displacement
Mr. Jones lives on the same road as the high school where he works. During his morning commute, Mr. Jones drives
two miles in two minutes to reach the donut shop. He spends six minutes at the shop and then realizes he’s forgotten
his lunch at home. He returns home, again covering two miles in two minutes. How should the data be graphed to
represent the motion of Mr. Jones’ car?
Which of the two graphs below is correct?
Both of these graphs are correct, but they provide different information. Graph 1 inFigure2.4 displays the distance
traveled by the car as a function of time, while Graph 2 inFigure2.5 displays the position of the car as a function