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Δ x = x f x 0 = 3 .5 m 1.5 m = + 2 .0 m . size 12{Δx=x"" lSub { size 8{f} } - x rSub { size 8{0} } =3 "." 5`m - 1 "." 5`"m "= +2 "." "0 m"} {}

In this coordinate system, motion to the right is positive, whereas motion to the left is negative. Similarly, the airplane passenger’s initial position is x 0 = 6 . 0 m and his final position is x f = 2 . 0 m size 12{x rSub { size 8{f} } =2 "." 0`m} {} , so his displacement is

Δ x = x f x 0 = 2 . 0 m 6 . 0 m = 4 . 0 m . size 12{Δx=x"" lSub { size 8{f} } - x rSub { size 8{0} } =2 "." 0`m - 6 "." 0`m= - 4 "." 0`m} {}

His displacement is negative because his motion is toward the rear of the plane, or in the negative x size 12{x} {} direction in our coordinate system.

Distance

Although displacement is described in terms of direction, distance is not. Distance is defined to be the magnitude or size of displacement between two positions . Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions . Distance has no direction and, thus, no sign. For example, the distance the professor walks is 2.0 m. The distance the airplane passenger walks is 4.0 m.

Misconception alert: distance traveled vs. magnitude of displacement

It is important to note that the distance traveled , however, can be greater than the magnitude of the displacement (by magnitude, we mean just the size of the displacement without regard to its direction; that is, just a number with a unit). For example, the professor could pace back and forth many times, perhaps walking a distance of 150 m during a lecture, yet still end up only 2.0 m to the right of her starting point. In this case her displacement would be +2.0 m, the magnitude of her displacement would be 2.0 m, but the distance she traveled would be 150 m. In kinematics we nearly always deal with displacement and magnitude of displacement, and almost never with distance traveled. One way to think about this is to assume you marked the start of the motion and the end of the motion. The displacement is simply the difference in the position of the two marks and is independent of the path taken in traveling between the two marks. The distance traveled, however, is the total length of the path taken between the two marks.

A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is her displacement? (b) What distance does she ride? (c) What is the magnitude of her displacement?

Two diagrams side by side. To the left is a horizontal line, or x axis, with points for final position and initial position. Displacement 1, shown by an arrow pointing leftward, equals negative 3 kilometers. Displacement 2, shown by an arrow pointing rightward, equals 2 kilometers. To the right is a pair of x and y axes, showing that east is the positive x direction and west is the negative x direction.

(a) The rider’s displacement is Δ x = x f x 0 = −1 km . (The displacement is negative because we take east to be positive and west to be negative.)

(b) The distance traveled is 3 km + 2 km = 5 km size 12{"3 km "+" 2 km "=" 5 km"} {} .

(c) The magnitude of the displacement is 1 km size 12{1" km"} {} .

Section summary

  • Kinematics is the study of motion without considering its causes. In this chapter, it is limited to motion along a straight line, called one-dimensional motion.
  • Displacement is the change in position of an object.
  • In symbols, displacement Δ x is defined to be
    Δ x = x f x 0 ,
    where x 0 is the initial position and x f is the final position. In this text, the Greek letter Δ (delta) always means “change in” whatever quantity follows it. The SI unit for displacement is the meter (m). Displacement has a direction as well as a magnitude.
  • When you start a problem, assign which direction will be positive.
  • Distance is the magnitude of displacement between two positions.
  • Distance traveled is the total length of the path traveled between two positions.

Conceptual questions

Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example.

Under what circumstances does distance traveled equal magnitude of displacement? What is the only case in which magnitude of displacement and displacement are exactly the same?

Bacteria move back and forth by using their flagella (structures that look like little tails). Speeds of up to 50 μm/s 50 × 10 6 m/s size 12{"50 μm/s " left ("50" times "10" rSup { size 8{ - 6} } " m/s" right )} {} have been observed. The total distance traveled by a bacterium is large for its size, while its displacement is small. Why is this?

Problems&Exercises

An x axis starts at 0 meters and ends at 12 meters. There are four points on the graph with displacement paths. Path A starts at 0 and stops at 7. Path B starts at 12 and ends at 7. Path C starts at 2, goes to 10, turns around and goes back to 8, then turns around again and stops at 11. Path D starts at 9, goes to 3, then turns around and stops at 5.

Find the following for path A in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

(a) 7 m

(b) 7 m

(c) + 7 m size 12{+7`m} {}

Find the following for path B in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Find the following for path C in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

(a) 13 m

(b) 9 m

(c) + 9 m size 12{+9`m} {}

Find the following for path D in [link] : (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.

Questions & Answers

Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
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