Position, Distance and Displacement


Q) A softball player leaves the batter's box, overruns first base by 3.0 meters, and then returns to first base. Compared to the total distance traveled by the player, the magnitude of the player's total displacement from the batter's box is

A. Smaller      B. Larger      C. The same

 Answer) A.

Q) A girl leaves a history classroom and walks 10. meters north to a drinking fountain. Then she turns and walks 30. meters south to an art classroom. What is the girl's total displacement from the history classroom to the art classroom?

A. 20. m south      B. 20. m north      C. 40. m north      D. 40. m south

Answer) A.

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Distance, Position, and Displacement

Motion is a change in the location of an object, as measured by an observer. Distance, in physics terms, means the total length of the path travelled by an object in motion. The SI metric base unit for distance is the metre (m). To help you understand the terms that describe motion, imagine that you are at your home in Figure 1.

Figure 1 Distance and direction along a straight line

You are at the location marked “0 m.” If you walk directly from home to your school in a straight line, you will travel a distance of 500 m.
If you walk from your school to the library and then return home, you will travel an additional distance of 700 m + 1200 m = 1900 m.
If your friend wants to know how to get to the library from your home, telling him to walk for 1200 m is not very helpful. You also need to tell your friend which direction to go. Direction is the line an object moves along from a particular starting point, expressed in degrees on a compass or in terms of the compass points (north, west, east, and south). Directions can also be expressed as up, down, left, right, forward, and backwards. Directions are often expressed in brackets after the distance (or other value). For example, 500 m [E] indicates that the object is 500 m to the east. 

Direction is important when describing motion. If the school in Figure 1 is your starting point, the library is in a different direction from your school than your home is. If the library is your starting point, then your school and home are in the same direction.

Scalar and vector Quantities

A scalar quantity is a quantity that has magnitude (size) only. Distance is an example of a scalar quantity. Since direction is so important in describing motion, physicists frequently use terms that include direction in their definitions. A vector is a quantity that has magnitude (size) and also direction. An arrow is placed above the symbol for a variable when it represents a vector quantity.

Position and displacement

Position is the distance and direction of an object from a particular reference point. Position is a vector quantity represented by the symbol $\vec{d}$. Notice the vector arrow above the symbol d. This arrow indicates that position is a vector: it has a direction as well as a magnitude. For example, if home is your reference point, the position of the school in Figure 2 is 500 m [E]. Note that the magnitude of the position is the same as the straight-line distance (500 m) from home to school, but the position also includes the direction (due east [E]). The position of the school from point 0 m can be described by the equation 

$\vec{d}_{school}$= 500 m [E]

Now assume that the library is your reference point, or the point 0 m. The position of the school from the reference point (library) can be described by the equation

$\vec{d}_{school}$= 500 m [E]

Once the position of an object has been described, you can describe what happens to the object when it moves from that position. This is displacement—the change in an object’s position. Displacement is represented by the symbol $\vec{\Delta d}$ .
Notice the vector arrow indicating that displacement is a vector quantity. The triangle symbol Δ is the Greek letter delta. Delta is always read as “change in,” so $\vec{\Delta d}$ is read as “change in position.” As with any change, displacement can be calculated by subtracting the initial position vector from the final position vector:

$\vec{\Delta d}$ = $\vec{d}_{final}$ - $\vec{d}_{initial}$

When an object changes its position more than once (experiences two or more displacements), the total displacement $\vec{d}_{T}$ of the object can be calculated by adding the displacements using the following equation:

$\vec{\Delta d}_{T}$ = $\vec{\Delta d}_{1}$  +  $\vec{\Delta d}_{2}$ 

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