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  • Define position, displacement, distance, and distance traveled.
  • Explain the relationship between position and displacement.
  • Distinguish between displacement and distance traveled.
  • Calculate displacement and distance given initial position, final position, and the path between the two.
Three people cycling along a canal. The blurred buildings in the background convey a sense of motion of the cyclists.
These cyclists in Vietnam can be described by their position relative to buildings and a canal. Their motion can be described by their change in position, or displacement, in the frame of reference. (credit: Suzan Black, Fotopedia)

Position

In order to describe the motion of an object, you must first be able to describe its position    —where it is at any particular time. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board. (See [link] .) In other cases, we use reference frames that are not stationary but are in motion relative to the Earth. To describe the position of a person in an airplane, for example, we use the airplane, not the Earth, as the reference frame. (See [link] .)

Displacement

If an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or a passenger moves toward the rear of an airplane), then the object’s position changes. This change in position is known as displacement    . The word “displacement” implies that an object has moved, or has been displaced.

Displacement

Displacement is the change in position of an object:

Δ x = x f x 0 , size 12{Δx=x rSub { size 8{f} } - x rSub { size 8{0} } } {}

where Δ x size 12{Δx} {} is displacement, x f size 12{x rSub { size 8{f} } } {} is the final position, and x 0 size 12{x rSub { size 8{0} } } {} is the initial position.

In this text the upper case Greek letter Δ size 12{Δ} {} (delta) always means “change in” whatever quantity follows it; thus, Δ x size 12{Δx} {} means change in position . Always solve for displacement by subtracting initial position x 0 size 12{x rSub { size 8{0} } } {} from final position x f size 12{x rSub { size 8{f} } } {} .

Note that the SI unit for displacement is the meter (m) (see Physical Quantities and Units ), but sometimes kilometers, miles, feet, and other units of length are used. Keep in mind that when units other than the meter are used in a problem, you may need to convert them into meters to complete the calculation.

The initial and final position of a professor as she moves to the right while writing on a whiteboard. Her initial position is 1 point 5 meters. Her final position is 3 point 5 meters. Her displacement is given by the equation delta x equals x sub f minus x sub 0 equals 2 point 0 meters.
A professor paces left and right while lecturing. Her position relative to Earth is given by x size 12{x} {} . The + 2 . 0 m size 12{+2 "." 0`m} {} displacement of the professor relative to Earth is represented by an arrow pointing to the right.

View of an airplane with an inset of the passengers sitting inside. A passenger has just moved from his seat and is now standing in the back. His initial position was 6 point 0 meters. His final position is 2 point 0 meters. His displacement is given by the equation delta x equals x sub f minus x sub 0 equals 4 point zero meters.
A passenger moves from his seat to the back of the plane. His location relative to the airplane is given by x size 12{x} {} . The 4 . 0 -m size 12{ - 4 "." 0"-m"} {} displacement of the passenger relative to the plane is represented by an arrow toward the rear of the plane. Notice that the arrow representing his displacement is twice as long as the arrow representing the displacement of the professor (he moves twice as far) in [link] .

Questions & Answers

what is ohm's law
Pamilerin Reply
states that electric current in a given metallic conductor is directly proportional to the potential difference applied between its end, provided that the temperature of the conductor and other physical factors such as length and cross-sectional area remains constant. mathematically V=IR
ANIEFIOK
A body travelling at a velocity of 30ms^-1 in a straight line is brought to rest by application of brakes. if it covers a distance of 100m during this period, find the retardation.
Pamilerin Reply
what is distribution of trade
Grace Reply
what's acceleration
Joshua Reply
The change in position of an object with respect to time
Mfizi
Acceleration is velocity all over time
Pamilerin
hi
Stephen
It's not It's the change of velocity relative to time
Laura
Velocity is the change of position relative to time
Laura
acceleration it is the rate of change in velocity with time
Stephen
acceleration is change in velocity per rate of time
Noara
what is ohm's law
Stephen
Ohm's law is related to resistance by which volatge is the multiplication of current and resistance ( U=RI)
Laura
how i don understand
Willam Reply
how do I access the Multiple Choice Questions? the button never works and the essay one doesn't either
Savannah Reply
How do you determine the magnitude of force
Peace Reply
mass × acceleration OR Work done ÷ distance
Seema
Which eye defect is corrected by a lens having different curvatures in two perpendicular directions?
Valentina Reply
acute astigmatism?
the difference between virtual work and virtual displacement
Noman Reply
How do you calculate uncertainties
Ancilla Reply
What is Elasticity
Salim Reply
using a micro-screw gauge,the thickness of a piece of a A4 white paper is measured to be 0.5+or-0.05 mm. If the length of the A4 paper is 26+or-0.2 cm, determine the volume of the A4 paper in: a). Cubic centimeters b). Cubic meters
Ancilla Reply
what is module
Alex Reply
why it is possible for an object(man) to stay on air without falling down?
akande Reply
its impossible, what do you mean exactly?
Ryan
Exactly
Emmanuella
it's impossible
Your
Why is it not possible to stand in air?
bikko
the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
Arzail
because of gravitational forces
Pamilerin
this mostly occur in space
Stephen
what is physics
Joshua Reply
no life without physics ....that should tell you something
Exactly
Emmanuella
😎👍
E=MC^2
study of matter and energy and an inter-relation between them.
Minahil
that's how the mass and energy are related in stationery frame
Arzail
Ketucky tepung 10m
firdaus
Treeskin, 6m Cloud gam water 2m Cloud gam white 2m And buur
firdaus
Like dont have but have
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Two in one
firdaus
Okay
firdaus
DNA card
firdaus
hey am new over hear
Shiwani
War right? My impesilyty again. Don't have INSURAN for me
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PUSH
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I give
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0kay
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Hear from long
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Hehehe
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All physics... Hahahaha
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Tree skin and two cloud have tokside maybe
firdaus
Sold thing
firdaus
PUSH FIRST. HAHAHAAHA
firdaus
thanks
firdaus
Kinetic energy is the energy due to montion of waves,electrons,atoms, molecule,substances an object s.
Emmanuella
Opjective 0
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Atom nber 0
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SOME N
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10.000m permonth. U use momentom with me
firdaus
hi
Hilal
plz anyone can tell what is meteor and why meteor fall in night? can meteor fall in the day
Hilal
meteor are the glowy (i.e. heated when the enter into our atmosphere) parts of meteoroids. now, meteoroids are the debris resulting from the collision of asteroids or comets. yes, it occurs in daytime too, but due to the daylight, we cant observe it as clearly as in night
Arzail
thank's
Hilal
hello guys
Waka
wich method we use to find the potential on a grounded sphere
Noman
hello
Pamilerin
Physics is the science that studies everything around us from the smallest things like quarks to the biggest things like galaxies. It's simply everything.
Laura
Good day everyone
Divine
It talks mainly about matter with related topics such as forces energy gravity and time. It's amazing
Laura
Hi
Alpha
Physics generally is the study of everything around us.
Steven
physics is the branch of sceince
shafiu
physics is the branch of sceince that deal with motion
shafiu
physics is the branch of sceince that deal with motion &energy
shafiu
Practice Key Terms 5

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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