Unit -2 Distance vs. Displacement...Value is always positive. Examples: distance, mass, temperature, time • Vector is a quantity that has direction. Value can be positive or negative.

Name: -----------

Unit -2

Date: _ 10/3 __ Period: ------

Distance vs. Displacement

Essential Questions:

• Why do we need 2 concepts for "how far" - distance vs.

displacement?

• How do we "measure" motion to communicate about it2

Questi-ons we ask about motion

• Where did the object start moving?

• When did the object start moving?

• How far did the object travel?

• How fast was the object moving?

• In what direction was the object moving?

~ Was the object speeding up or slowing down?

The motion equations help to answer these' questions & make

predictions about motion

Formulas d

Average Speed = .6.t

!'iv Average Accderation = !'it

Average Velocity = ~" - et

vi + vf Average Velocity = ~-~

2

r - , ---,.Slide 2

1 ~·

O_bjectives

.. Explain the Greek symbol "delta" or~ This symbol appears a lot in physics and mathl

• Define dist~nce

• Define-displacement

• Explain the difference between a scalar vs. v~ctor -which is-distance and which is displacement-'?

Review: What is Hposition"?

" Position or "x" is the location of the object on a coordinate systems ( or "number line").

Os ls 2s

0 Question: What is th~osition of the runner at.Os? Vm

., Question: What is the position of the runner at 2s?

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sliae3

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2 ~·

What is "delta" or~?

" ~ means '-'subtraction"

• What are you subtracting? - -It depeuds .Qn the variable after~: _

Formulas d

Average Speed= Lit

c'.', v A1,erage Acceleration = .:"It

A v·1· L'i.X , 1-..vernge e oc1ty = L'i..t

~t means "subtract two time ·instants"

Llx means "subtract two positions"

~v means "subtract two velocities"

v- = v-+ ~ t t ' -

Ayerage Velocity = V; + ""ir 2

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A Tens you to subtract "initial" and ''finarJ values· 0 ~ means subtraction of

"end value" - "start value"

.. "end value" is called "final" or "f' e.g., x1 means "final position"

" "start value" is called "initial" or "i" e.g. , xi means "initial position"

Note: Initial means "start" NOT your name initials!

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~ Tells you to subtract Hinitial" and Hfina!" vaJues

• !J.. means subtraction of "initial value" - "final "9ffle"

Today we will focus on 6.x

• What values are you subtracting? It depends on the variable after ~:

.At means "subtract two time instants"

!J..x means "subtract two positions"

.ti v means "subtract two velocities"

Distance vs. Disp~acement

.. Distance is the total length of your actual path Symbol: "d"

., Displacement is the straight path from start to finish Symbol: "!J..x" Math definition: 11,1: = x 1 - xi Conceptual Example:

d is the actual path you took.

L1x is the displacement - straight path from initial position to final position

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Practice 1

Frank walks from x1 to x2

a)What is the distanced he travels? __ 1/,____D;_.n-J------=---

b) What is· his displacement fix? tix = x2 - x1 = -20m - (25"rrij

~ -45"m \

clire,.of,

----t--f---+---t----i------il,llill--+---+--+-----!, ___ .....__, X (m) -20 -10 0 10 20

Practice 2

Frank then walks from x2 to x3.

a)What is the distanced he travels? 25' rYJ b )What is his displacement ll.x?

30

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.6x = X3 - X2 = sty) - (- z o JY1) = s rvr -t -zo/11 = 25"" I">)

~-7 . ............. :....-----'~---'----r ..... ;,_=~-=-=~--===·==

-- I I I I ' ---1 x(m) -20 -10 0 10 20 30

Slide 10

~-tu~ (!)r"'

a.n--J.oU41& ,-

Di rco(\..o"' (/.1 1'? ~ n'#

Ma~ '-fuOfl. (,.,d

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Practice 3

Consider Frank's total trip from x1 to x3.

a)What is1he distanced hetra-vels? '/~I"? + 2 S-PJ b)What is his clisplacement Ax? ~ rO'>,

""ac X3 ~xi~ 5' WI - (2s /o/1) = i 3 D;r,) ,r.c; f'lvz.. /"Y7 Ct.~ ,· ~

X2 X3 /

Practke 3

Draw the displacement of Frank's total trip from x1 to x3 as an arrow that points from start to finish:

X2 X3 LlXtrJr X1 ~ It

' - I I .. r ' -20 -10 0 10 20 30 All vectors are drawn as arrows to show the direction.

Displacement is an example of a vector!

Practice 3 - Ans'1ver

1 X (m)

Slide 13

Draw the displacement of Frank's total trip from x 1 to x3 as an arrow that points from start to finish: }"\.. c. . ,;d ,..

CX j,-~ °"'t:,~ ~~ ,rivf:/' I __ _ X2 · X3 -20 m X 1 ..,_ ,;

,,,. "' ~"""""-===-==--"""""=a"""""' _______ """

----i---+-+----+----+-----ii,ffl-. --+-1-----+--l,~-. .-+I X (m) -20 -10 0 10 20 30

Displacement is an example of a vector!

Every kind of vector has a magnitude (how much) and direction (where):

Example: -20 m is a displacement with a magnitude of 20m and a negative direction (to the left).

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Exit Ticket

Trish, Mike, and Juan-leave the park to go to a pizza shop. Trish takes path A, J~n takes path B, and ~ takes path C. Mi)G(._

Jua:4\

1. Who travels the longest distanced? _A _____ _ 2. Who has the largest displacement Ill..? SQft-1