# Release verification 6-23  (Page 2/7)

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$\Delta x={x}_{f}-{x}_{0}=3\text{.5 m}-1.5 m=+2\text{.0 m}.$

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 ${x}_{0}=6\text{.}0 m$ and his final position is ${x}_{f}=2\text{.}0 m$ , so his displacement is

$\Delta x={x}_{f}-{x}_{0}=2\text{.}0 m-6\text{.}0 m=-4\text{.}0 m.$

His displacement is negative because his motion is toward the rear of the plane, or in the negative $x$ 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?

(a) The rider’s displacement is $\Delta x={x}_{f}-{x}_{0}=\text{−1 km}$ . (The displacement is negative because we take east to be positive and west to be negative.)

(b) The distance traveled is $\text{3 km}+\text{2 km}=\text{5 km}$ .

(c) The magnitude of the displacement is $1 km$ .

## 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 $\Delta x$ is defined to be
$\Delta x={x}_{f}-{x}_{0},$
where ${x}_{0}$ is the initial position and ${x}_{f}$ is the final position. In this text, the Greek letter $\Delta$ (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 $\text{50 μm/s}\phantom{\rule{0.25em}{0ex}}\left(\text{50}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m/s}\right)$ 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

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) $+7 m$

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) $+9 m$

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.

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s.
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so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
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SUYASH
What is lattice structure?
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Ebrahim
or in general
Ebrahim
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s.
Graphene has a hexagonal structure
tahir
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Cied
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Yasmin
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Cesar
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Uday
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
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Prasenjit
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Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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Damian
silver nanoparticles could handle the job?
Damian
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Azam
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Uday
I'm interested in Nanotube
Uday
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Prasenjit
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
how did you get the value of 2000N.What calculations are needed to arrive at it
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