Math tools:

I. __________________ figures (digits)

- tell you how ___________ a measurement is

- _________ figures ________ precise

Ex: It is not that useful to

say that your height is

______________________

inches because your

height _____________ by

at least an ____________

during the day.

Ex 1: Measure the length of a box:

L

L =

last digit is _____________

1 2 3 4 5 6

Ex 2: Use a “better” ruler:

L

L =

last digit is ______________

1 2 3 4 5 6

Ex 3: Measure the length of a different box:

L

L =

1 2 4 5 6 7

The precision is worthless because answer is_____________—not close to true or actual value.

A. Figures (numbers) are significant if they are:1. ________________ numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9

2. any zeros that are:

a/ between any _________________ numbers: 509; or

b/ to the ___________ of a non-zero number AND

to the ___________ of the decimal point: 0.00790; or

c/ between a non-zero number and the __________

_________ : 10.

number # sig. figs.

number # sig. fig.

5.3 6.6070

202900 3.00 x 108

0.008 40

0.67 40.

Ex:

B. Sig. figs. when multiplying or dividing:

C. Sig. figs. when adding or subtracting:

3.73 x 5.7 = 21

____ sig. figs.

____ sig. figs.

answer hasthe _________number of sig. figs., in thiscase: ____

3

2

lower

2

18.541+106.6 125.1

___ decimal places___ decimal places

answer has the _________number of ___________________ ,in this case: ____

3

1

lowerdecimal places

1

II. Standard Scientific Notation:

A. Moving the decimal point to left

B. Moving the decimal point to right

616000 = 6.16 x 10

________ decimal pt.

Shift ______ to here by ___ places

implied5

exponent is ___________b/c number is _____ 1

positive

>

0.0070 = 7.0 x 10exponent is ___________b/c number is _____ 1

negative

<

5

-3

left

Shift ______ to here by ___ places3

right

Ex: Convert to standard scientific notation

number scientific notation

43000

0.0290

2012

0.5

80

80.

4.3 x 104

2.90 x 10-2

2.012 x 103

5 x 10-1

8 x 101

8.0 x 101

I. Units: In Regents Physics, we almost

always use the _____ (International System)

metric system. The ___________________ ,or

most basic, units in this system are:

SI

quantity unitabbrev-iation

length meter

current ampere

time second

mass kilogram

m

A

s

kg

The abbreviations spell _______________ (almost)"mAsk"

fundamental

I. Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed.

1 bottom

Ex: d = 15 nm rewrite as: d = 15 x _____ m

prefix _________

represents ____

with prefix without

5.3 km

1.7 cm

2.00 s

1.21 GW

8.6 kg

A trick b/ckg is alreadyan SI unit

__________ for

length (meters)

I. Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed.

1 bottom

Ex: d = 15 nm rewrite as: d = 15 x _____ m

symbol SI unitprefix _________

represents ____10-9

10-9

with prefix without

5.3 km

1.7 cm

2.00 s

1.21 GW

8.6 kg

5.3 x 103 m1.7 x 10-2 m

2.00 x 10-6 s

1.21 x 109 W

8.6 kg

A trick b/ckg is alreadyan SI unit

__________ for

length (meters)

V. Converting Units: the power of "one"

Ex: Convert 60 miles to kilometers.Use the conversion factor: 1 mi =__________ km This can be written as either:

or

Multiplying by either of these two factors does

not change the ________________ (only the units)

because both factors equal _______ .

Write: 60 mi x _________ = km96.54

~100 km

1.609 km

1 mi

1.609

1.609 km

1 mi 1.609 km1 mi

one

actual value

VI. Slope = m = ________y

x

10

20

40

30

2 4 6 8

Steps:

1. Draw a best fit line using a __________

1. Use two points on the

line to calculate m:

m = y = x

= ________

=

y2 – y1

x2 – x1

(x2, y2) = ( , )

(x1, y1) = ( , )

8 32

1 5

00

ruler

Steps:

1. Draw a best fit line using a __________

1. Use two points on the

line to calculate m:

32 - 58 - 1

3.9

In PhysRT:

I. Distances and displacements

Distance is ______________________________________

or __________________________________________________

Instead of _____________ , we will use _______ for

distance. We will use SI (international system)

units. The SI unit for distance is the _____________ .

Any other unit for distance must first be____________

________________________ before using any equation in

Regents Physics.

initialposition

finalposition

change in position =

______________– quantities with ______________(size) only

Ex: distance d = 2.0 m

____________– quantities with magnitude and _________

Ex: displacement d = 2.0 m, west

Vectors are represented by ________________:

Distance d is a _______________.

Displacement d is a_____________________ .

distance =

•must have arrow __________ for_________________

•use a ___________ to draw to scale as a straight line

•right or up is______________; down or left is ___________

•right =___________; up =_______________, etc

•any vector with same mag. and dir. is_______________

Ex: Draw d = 2.0 m, west. Use a scale of 1cm:1 m.

Ex: The vectors below are all _________________ because

they have the same _______________ and _______________:

II. Adding Vectors

add using the ______________________method.

draw the _________________displacement ______ as

an ____________ from the ________ of A to the ________ of B

A = 2 m, E B = 3 m, E

Ex: Use a ruler to draw the vectors to the scale: 1 cm:1 m

A B

Resultant R = _________

R = _____________

Total distance traveled = _________

Resultant displacement =____________

Ex:

Ex. What is B + A = ?AB

R = _____________

The __________________ displacement R =__________

magnitude of R: ___________

direction of R: _____________Notice that this new R is same as _________________

The ________________ in which vectors are added

__________________________ . This is true even if

you add ________________________________________ .

Ex: If A = 3 m, east

Then –A = ___________

or = _________ (the ____________sign shows direction)

If X = Then -X =

Compared to X, -X has the same ________________ ,

but the opposite _____________________ .

Find A – B = ____________

A = 2 m B = 3 m

A + (-B):

R =_________ = _________

Total distance traveled =___________

but resultant displacement = ______________

III. Subtracting vectors using the head to tail method.

Given:

mag. = ________

dir. = ________

Ex: Using same vectors, what does B – A = ?

B = 3 m A = 2 m

B – A =_____________

R = __________ = _________

Total distance covered = ______________

Resultant displacement =______________Notice that the ____________________ here is exactly

__________________ to the one in the previous example.

C

D Find C + D.

mag. of R = ____________

=___________

IV. Adding non-parallel vectors.

dir. of R:

starthere

R =_________________

Total distance =____________

Ex: What is D + C?

R =__________________

starthere

R could also be written:

R = _______________________________________

mag. of R = ____________

=___________

dir. of R:

Ex. Find C – D

R = __________________

D

C

Total distance =____________

starthere

mag. of R = ____________

dir. of R:

IV. Subtracting non-parallel vectors.

Ex. Draw D- C

R = __________________

DC:

Total distance =____________starthere

mag. of R = ________

dir. of R:

I. Time t is___________________________________It is a _____________________________

In physics, the time between two ___________ isis called the ___________________________ .

event 1occurs at t =

event 2occurs at t =

ti = ____________ time =

tf = ____________ time =

For example, if…

Then the time interval: tf – ti = t equals

In Regents Physics, instead of ________ , we use

the symbol _____ for time intervals and often just

call it the ____________ . Remember that _____

represents ____________________________________ .

The basic unit for time is the __________________ .

Other units, such as ___________________________

must usually be converted into _________________

before solving any problems.

t = tf – ti =

The time interval will always be ______________ .

II. speed v = _______________________________

=________________________________

=_________________________________

Ex:

Equation for v from PRT

(Physics Reference Tables):

Speed v can be ______________ (not changing), or

it can change. If it changes, the speed at any

instant is called the ____________________ speed.

The ______________speed, vavg = v is:

…the 4 _____________________ (basic) units:

Ex: Jenny runs 95 meters in 15 seconds.

Find her average speed. Show all work.

____________ units are madeup of…..

Ex. A car, initially moving at a speed of 25 m/s,increases its speed to 45 m/s in 3.0 seconds. What is its average speed during the 3.0 s?

vi = ____________ speed =

vf = ____________ speed =

This equation is NOT

in your PRT. You must

_____________________ .

Word problem hints:

1/ If an object starts from rest: vi =

2/ If an object comes to rest: vf =

3/ If the speed of an object does NOT change,

v =

How far will the car in the last example

travel in 12 seconds?

Given:

Unknown:

Ex. Units for speed v: units of ______________units of speed =

units of ______________

[v] =

Put a rectangle around units of distance,and an oval around units of speed:

m cm/s km/h mi

1/s ft/s in m/s2

mph km in/y m/s

cm h s km/h

III. velocity v = _________________________________

mag. of the velocity = the ____________

Ex:

= ________________________________ __________________________________

velocity = ___________ + ________________

Draw velocity as an _________:

=

average velocity:

Ex: Godzilla moves 5.0 x 102 meters east in 2.0 seconds. Find his average velocity.

If you assume that east is positive, you maywrite this velocity as:

Note: Speed and velocity have same _________

and use the same_______________:

Ex: Ms. Rudd walks 1) 6.0 m east in 4.0 s, then runs 2) 2.0 m west in 0.50 s. Find her average speed in each part, and 3) the average speed over the entire time.

1) v = d/t

v = d/t

v = d/t

2)

3)

Why is the average speed over the entire timecloser to the answer for part _____ ?

d = the _____________ distance

Now find the average velocities for each part ofthe previous example.

1) v = d/t

v = d/t

v = d/t

2)

3)

d = the __________________ here

d = _______________ d:

Why is the answer to 3) now ________ than what it was on the last slide?

Uniform

motion

constant ________________

constant ______________

in______________________

Ex. A car leaks oil at a constant rate while

moving to the right in uniform motion. Sketch

the pattern of drops it leaves behind.

IV. Uniform motion:

or….

acceleration, a = ____________________________

=______________________________

average a = where Δv =

Any time that _____________ changes, thereis___________________. And because:

velocity = +

changing either _____________ or ______________or _________ results in acceleration. In thissection, we only consider changes in __________ .The _________ speed changes, the _________ the a.

Ex: Ms. Rudd accelerates her jet skis from a speed of 5.0 m/s to a speed of 17 m/s in 3.0 s. Find the magnitude of her acceleration.

SI units for a:

other units:

Using brackets [ ] for units:

[a] =

From last problem:

a =

_________gainedeach _________

Because a = _________ , the ________________

of a is the same as the __________________

of the ________________in v: v = vf - vi.

v =

Sincev ____ 0 (which is _________________),

then also the acceleration a ____ 0.

Ex 1: An object moving to the right

accelerates to a faster speed.

Ex 2: An object moving to the right is

slowing down, or ________________________.

v =

Sincev ____ 0, then also a ____ 0.

Note that the direction of the acceleration

______________ always the same as the

direction of the ___________________ .

Conclusions:1. If the ___________ and the________________ are in the __________ direction, then the object is _________________ ( __________________). 2. If the ___________ and the________________ are in _______________ directions, then the object is _________________ ( __________________).

Ex 3: An object moving up but slowing down:

v =

a is ______________ or_______________.

_______________can be confusing, but remember:

1. The __________________ is always from the

_________________ to the _____________ points.

1.The ________________ always has the same

direction as the object's ____________________

(the _________ direction it __________________).

1.The ___________________ has a direction givenby the direction of the ____________ in the ______________ , which may or may not be thesame as the direction of the ________________ .

a = 2.0 m/s2, east =

Ex: The _________________of the acceleration is

also called the ____________________.

scalar

…is the magnitude

of the…

vector

distance

speed

acceleration

In review:

In word problems, remember:

1) “starts from rest” means

2) “comes to rest” means

1) When an object is in ______________motion,it means it has a _________________velocity. In that case: __________ and ____ = _____ = _____

1) up/right are___________________,

1) down/left are____________________.

Examples: The speed of _____________________given in the PhyRT are ___________________.

Ex: A ball is dropped. It accelerates from rest to a speed of 29 m/s in 3.0 seconds. Finds its acceleration.

What are the magnitude and direction of a?

How much speed does the ball gain each second?

Ex: What is the speed of a giraffe, initially movingat a speed of 21 m/s, that accelerates at 5.0 m/s2 for 2.0 s?

If it remains at this final speed, how long will ittake to travel 100. m?

Ex: Chuck Norris accelerates from a speed of 4.0 m/s to 10. m/s in 4.0 seconds. Find his average speed during that time.

How far does he travel in the 4.0 s?

Why can't you use vi or vf to find d in this case?

Graphical Analysis of motion in _________________

I. Distance and displacement.

What is the total distance moved?What is the resultant displacement?

d (m)

t (s)

20

10

5 10 15

Find the average speed in the 0-5 s interval.

Repeat for 5-10 s and 10-15 s.

II. Uniform motion – ____________ is constant

d

t

slope =_____ = ________

slope =______________

speed = _______________

A. Graph of d vs. t

What would the graph of a slower object look like?

________d in each _____

How much slower is B?1 2

v

t

B. Graph of speed __________ for uniform motion

slope =______

slope =________________

a =_________

What does the area shown represent?

area = L x W = = _____________ =_____________

units: ______ x ______ = _________

What about B?

slope =______

a

t

C. Graph of a vs. t for uniform motion

In review: for __________________ Motion:

d

t t

v a

t

How would you graph B?

paper

tape constant v

timer marks the tape at constant ________ intervals

As car moves, describe pattern of marks on tape.

Ex: tape timers

_____________ spaced b/c car moves the __________ d between each mark.

cart pulls tape________________

How would tape look if car was twice as fast?

III. Non-uniform motion: ___________________ acceleration

d

t

slope of tangent is the______________________

The slope ___________

b/c speed v ___________

A. Graph of d vs. t for object beginning at rest

0

Object covers ________ din each________________

dashed linesare__________

________speed vi = ___ __________________

v

t

A. Graph of speed v vs. t for __________________acceleration a beginning _______________ .

slope =________

= __________

slope = _______________

a = ______________

What does the area shown represent?

area = (1/2) bh = (½) ______________=__________

units: ______ x ______ = ______

a

t

C. Graph of a vs. t for constant a

In review: For _________________________acceleration

d

t

v

t

a

t

cartpaper

tape

As car moves, describe pattern of marks on tape.

Ex:

_______________ spaced b/c car moves _________distance d between each mark.

Timer tape for ___________________

How would tape look if car had more acceleration?

timer

Compare ____________ to ________________motion:

d

t t

v a

t

d

t

v

t

a

t

Ex. Answer the questions based on the graph atright.

d (m)

4

2 4 6t (s)

-8

What is the total distance traveled?

What is the resultant displacement?

Find the average speed in the first 2 s.

Find the average speed over the entire 6 s.

Find the average velocity over the entire 6 s.

0

Ex: The graph below describes a UFO moving in a straight line.

A B

C

Find vavg, d, and a in regions A, B and C.

t (s)

v(m/s)

4.0 8.0 12

20.

40.