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Position, Displacement, and
Average Velocity
By the end of this section, you will be able to:
• Define position, displacement, and distance traveled.
• Calculate the total displacement given the position as a function of time.
• Determine the total distance traveled.
• Calculate the average velocity given the displacement and elapsed time.
When you’re in motion, the basic questions to ask are:
Where are you? Where are you going? How fast are you
getting there? The answers to these questions require that
you specify your position, your displacement, and your
average velocity—the terms we define in this section.
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Position
To describe the motion of an object, you must first be able to
describe its position (x): where it is at any particular time.
More precisely, we need to specify its position relative to a
convenient frame of reference. A frame of reference is an
arbitrary set of axes from which the position and motion of an
object are described.
For example, a cyclist’s position could be described in terms of where she is in
relation to the buildings she passes Figure 3.2. In other cases, we use reference
frames that are not stationary but are in motion relative to Earth. To describe the Figure 3.2 These cyclists in
position of a person in an airplane, for example, we use the airplane, not Earth, Vietnam can be described by
as the reference frame. To describe the position of an object undergoing one- their position relative to buildings
dimensional motion, we often use the variable x. Later in the chapter, during the or a canal. Their motion can be
discussion of free fall, we use the variable y. described by their change in
position, or displacement, in a
frame of reference. (credit:
modi[cation of work by Suzan
Black)
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Displacement
If an object moves relative to a frame of reference—for example, if a
professor moves to the right relative to a whiteboard Figure 3.3—then
the object’s position changes. This change in position is called
displacement. The word displacement implies that an object has
moved, or has been displaced.
Although position is the numerical value of x along a straight line
where an object might be located,
displacement gives the change in position along this line.
Since displacement indicates direction, it is a vector and can be either
positive or negative, depending on the choice of positive direction.
Also, an analysis of motion can have many displacements embedded in
it. If right is positive and an object moves 2 m Figure 3.3 A professor paces left and
to the right, then 4 m to the left, the individual displacements are 2 m right while lecturing. Her position
and -4 m, respectively. relative to Earth is given by x. The
+2.0-m displacement of the professor
relative to Earth is represented by an
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Figure 2.3 The displacement vector from point
A (the initial position at the campsite) to point B
(the final position at the fishing hole) is
indicated by an arrow with origin at point A and
end at point B. The displacement is the same
for any of the actual paths (dashed curves) that
may be taken between points A and B.
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Displacement, which is the change in position of an
object in a given direction. The symbol for
displacement is d , where the Greek letter delta “ △”
indicates change. Figure 2 illustrates a displacement
that occurs in moving from one position, d 1, to
another, d2, relative to an observer.
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What is speed?
Speed is the quantity that tells us
how fast something is moving.
To calculate the other physical quantities in kinematics we must introduce the time variable. The time
variable allows us not only to state where the object is (its position) during its motion, but also how fast it
is moving. How fast an object is moving is given by the rate at which the position changes with time.
It is also
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What is velocity and when we talk about it?
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Average Velocity
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Describing Acceleration
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v There is acceleration when velocity increases or decreases over time.
For an object whose velocity decreases over time, we can say that it is
undergoing deceleration or retardation.
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Two Kinds of Acceleration
Uniform acceleration Nonuniform acceleration
An object undergoes uniform acceleration when An object undergoes non-uniform acceleration if
the change (increase or decrease) in its velocity the change in its velocity for every unit of time is
for every unit of time is the same (Table 2.3). not the same (Table 2.5)
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