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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)


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] .)


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 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 motion
Ali Reply
When a body changes its position with respect to its surroundings then it is said to be in motion
it is a change in position, direction, shape and arrangement of a body or an object which is initially at rest
Pls guys am having problem on these topics: latent heat of fusion, specific heat capacity and the sub topics under them.Pls who can help?
hamidat Reply
Thanks George,I appreciate.
this will lead you rightly of the formula to use
Most especially it is the calculatory aspects that is giving me issue, but with these new strength that you guys have given me,I will put in my best to understand it again.
you can bring up a question and let's see what we can do to it
I also have a problem with the calculation sincerely
the distance between two suasive crests of water wave traveling of 3.6ms1 is 0.45m calculate the frequency of the wave
Idris Reply
v=f×lemda where the velocity is given and lends also given so simply u can calculate the frequency
You are right my brother, make frequency the subject of formula and equate the values of velocity and lamda into the equation, that all.
lExplain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.
Christoper Reply
When light is reflected at Brewster's angle from a smooth surface, it is 100% polarizedparallel to the surface. Part of the light will be refracted into the surface.
What is specific heat capacity?
hamidat Reply
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
formula for measuring Joules
Rowshan Reply
I don't understand, do you mean the S.I unit of work and energy?
what are the effects of electric current
What limits the Magnification of an optical instrument?
Naeem Reply
Lithography is 2 micron
what is expression for energy possessed by water ripple
Prabesh Reply
what is hydrolic press
Mark Reply
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
what is dimensional unite of mah
Patrock Reply
i want jamb related question on this asap🙏
sharon Reply
What is Boyles law
Pascal Reply
it can simple defined as constant temperature
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
what is motion
Mua Reply
getting notifications for a dictionary word, smh
what is escape velocity
Shuaibu Reply
the minimum thrust that an object must have in oder yo escape the gravitational pull
what is a dimer
what is a atom
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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