# 2.1 Displacement  (Page 2/7)

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Note that displacement has a direction as well as a magnitude. The professor’s displacement is 2.0 m to the right, and the airline passenger’s displacement is 4.0 m toward the rear. In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction). The professor’s initial position is ${x}_{0}=1\text{.}5\phantom{\rule{0.25em}{0ex}}\text{m}$ and her final position is ${x}_{\text{f}}=3\text{.}5\phantom{\rule{0.25em}{0ex}}\text{m}$ . Thus her displacement is

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

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.

it is a process in which electrolyte breaks down into its ions....
ionization
Shang
A ball is thrown vertically upwards so that its max height is 100m...at the same instant another ball is dropped frm 100m above the ground...where will the two balls meet and why?
50m
wenhe
why?
Blessing
Blessing
😟
Blessing
75m
S.M
how?😨
Blessing
because they approach each other at different speeds, but same acceleration, so you can calculate its height above ground.
S.M
Yeah. He's right. Your question seems very similar to a question I did in physics class, and our answer was 50.so yeah that's why I said that. But 75m is correct
wenhe
what's is waves
Waves is the disturbance of a medium such that the particles in the medium vibrate to cause the movement of energy from one point to another without the the particle itself moving.
Prince
what is the medium that light waves travel through?
Luke
and electrons, protons, neutrons and quarks for that matter?
Luke
it's spacetime that light and every other particles travel through actually
S.M
ether
Anand
for above question, i think 50m is the correct answer. the first ball will behave exactly like 2nd ball when it reaches 100m (max height).
James
From rest, a body moves with an acceleration of 8m/s in 10 secs. calculate the distance during the 8th seconds
Caleb
please use energy conservation to solve this problem. i think i have an answer but it is too long to explain here.
James
one is with some initial velocity v, while other one will start it's journey from rest, so they can't travel equal distance in equal amount of time
S.M
to be honest I knew the answer was just pointing out a flaw in above answer and light does not require a medium to travel through, this was proved in the 1887 by Michelson and Morley.
Luke
the two balls have different acceleration. the accelerations are same in magnitude but in different directions for them. so the first ball will gradually move slower and the 2nd ball will move faster.
James
u can just put 50m or 75m in equation to check whether right or not
James
the total energy of the two balls are equal, KE + PE. 1/2mv(1)^ 2 + mgh(1) = 1/2mv(2)^2 +mgh(2). use that
James
what's is electrolysis
Give an example (but not one from the text) of a device used to measure time and identify what change in that device indicates a change in time.
hour glass, pendulum clock, atomic clock?
S.M
tnks
David
A heart pumping blood would indicate a change in time as its volume or pressure changed. The ratio of displacement or change in configuration between any 2 systems can indicate time.
Khashon
how did they solve for "t" after getting 67.6=.5(Voy + 0)t
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.
the topic is kinematics
David
can i get notes of solid state physics
Lohitha
just check the chpt. 13 kinetic theory of matter it's there
David
is acceleration a fundamental unit.
no it is derived
Abdul
no
Nisha
K thanks
David
no it's not its derived
Emmanuel
hi
Hello
Emmanuel
hello
David
Hello Emmanuel
Emmanuel
I'm good
that's good
Emmanuel
how are you too
am cool
Emmanuel
spending time summarizing
Emmanuel
Emmanuel
I am fin
Longwar
ok
hi guys can you teach me how to solve a logarithm?
how about a conceptual framework can you simplify for me? needed please
Villaflor
Hello what happens when electrone stops its rotation around its nucleus if it possible how
Afzal
I think they are constantly moving
Villaflor
yep what is problem you are stuck into context?
S.M
not possible to fix electron position in space,
S.M
Physics
Beatriz
yes of course Villa flor
David
equations of kinematics for constant acceleration
A bottle full of water weighs 45g when full of mercury,it weighs 360g.if the empty bottle weighs 20g.calculate the relative density of mercury and the density of mercury....pls I need help
well You know the density of water is 1000kg/m^3.And formula for density is density=mass/volume Then we must calculate volume of bottle and mass of mercury: Volume of bottle is (45-20)/1000000=1/40000 mass of mercury is:(360-20)/1000 kg density of mercury:(340/1000):1/50000=(340•40000):1000=13600
Sobirjon
the latter is true
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture...take density of water as 1g/cm3 and density of liquid 1.2g/cm3
Lila
plz hu can explain Heisenberg's uncertainty principle
who can help me with my problem about acceleration?
ok
Nicholas
how to solve this... a car is heading north then smoothly made a westward turn during the travel the speed of the car remains constant at 1.5km/h what is the acceleration of the car? the total travel time of the car as it smoothly changed its direction is 15 minutes
Vann
i think the acceleration is 0 since the car does not change its speed unless there are other conditions
Ben
yes I have to agree, the key phrase is, "the speed of the car remains constant...," all other information is not needed to conclude that acceleration remains at 0 during the entire time
Luis
who can help me with a relative density question
Lila
1cm3 sample of tin lead alloy has mass 8.5g.the relative density of tin is 7.3 and that of lead is 11.3.calculate the percentage by weight of tin in the alloy. assuming that there is no change of volume when the metals formed the alloy
Lila
So it looks like you need a formula for rotational acceleration. Are you asking about its angular acceleration?
Khashon
morning, what will happen to the volume of an ice block when heat is added from -200°c to 0°c... Will it volume increase or decrease?
no
Emmanuel
hi what is physical education?
Kate
BPED..is my course.
Kate
No
Emmanuel
I think it is neither decreases nor increases ,it remains in the same volume because of its crystal structure
Sobirjon
100g of water is mixed with 60g of a liquid of relative density 1.2.assuming no changes in volume occurred,find the average relative density of the mixture. take density of water as 1g/cm3 and density of liquid as 1.2g/cm3
Lila
Sorry what does it means"no changes in volume occured"?
Sobirjon
volume can be the amount of space occupied by an object. But when an object does not change in shape it will still occupy the same space. Thats why the volume will still remain the same
Ben
Most soilds expand when heated but if it changes state at 0C it will have less volume. Ice floats because it is less dense ie a larger mass per unit volume.
Richard
how to calculate velocity
v=d/t
Emeka
Villaflor
Villaflor
v=d/t
Nisha
hello bro hw is life with you
Mine is good. How about you?
Chase
Hi room of engineers
yes,hi sir
Okwethu
hello
akinmeji
Hello
Mishael
hello
Jerry
hi
Sakhi
hi
H.C
so, what is going on here
akinmeji
Ajayi
good morning ppl
ABDUL