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 _____________

Ex 2: Use a “better” ruler: L L = last digit is ______________

Ex 3: Measure the length of a different box: L L = 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: 5 0 9; or b/ to the ___________ of a non-zero number AND to the ___________ of the decimal point: ; or c/ between a non-zero number and the __________ _________ : 1 0. number # sig. figs. number # sig. fig x Ex:

B. Sig. figs. when multiplying or dividing : C. Sig. figs. when adding or subtracting : 3.73 x 5.7 =21 ____ sig. figs. answer has the _________ number of sig. figs., in this case: ____ 3 2 lower  ___ decimal places answer has the _________ number of ___________________, in this case: ____ 3 1 lower decimal places 1

II. Standard Scientific Notation: A. Moving the decimal point to left B. Moving the decimal point to right = 6.16 x 10 ________ decimal pt. Shift ______ to here by ___ places implied 5 exponent is ___________ b/c number is _____ 1 positive > = 7.0 x 10 exponent is ___________ b/c number is _____ 1 negative < 5 -3 left Shift ______ to here by ___ places 3 right

Ex: Convert to standard scientific notation numberscientific notation x x x x x x 10 1

I. Units: In Regents Physics, we almost always use the _____ (International System) metric system. The ___________________,or most basic, units in this system are: SI quantityunit abbrev- iation lengthmeter currentampere timesecond masskilogram 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 prefixwithout 5.3 km 1.7 cm 2.00  s 1.21 GW 8.6 kg A trick b/c kg is already an 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 unit prefix _________ represents ____ with prefixwithout 5.3 km 1.7 cm 2.00  s 1.21 GW 8.6 kg 5.3 x 10 3 m 1.7 x m 2.00 x s 1.21 x 10 9 W 8.6 kg A trick b/c kg is already an 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 _________ = km ~100 km km 1 mi km 1 mi km 1 mi one actual value

VI. Slope = m = ________ yy xx Steps: 1. Draw a best fit line using a __________ 1.Use two points on the line to calculate m: m =  y =  x = ________ = y 2 – y 1 x 2 – x 1 (x 2, y 2 ) = (, ) (x 1, y 1 ) = (, ) ruler Steps: 1. Draw a best fit line using a __________ 1.Use two points on the line to calculate m:

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. initial position final position 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 = ? A B 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 mA = 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:  start here R =_________________ Total distance =____________

Ex: What is D + C? R =__________________ start here R could also be written: R = _______________________________________ mag. of R = ____________ =___________ dir. of R: 

Ex. Find C – D R = __________________ D C Total distance =____________ start here mag. of R = ____________ dir. of R:  IV. Subtracting non-parallel vectors.

Ex. Draw D- C R = __________________ D C: Total distance =____________ start here mag. of R = ________ dir. of R: 

I. Time t is___________________________________ It is a _____________________________ In physics, the time between two ___________ is is called the ___________________________. event 1 occurs at t = event 2 occurs at t = t i = ____________ time = t f = ____________ time = For example, if…

Then the time interval: t f – t i =  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 = t f – t i = 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, v avg = v is:

…the 4 _____________________ (basic) units: Ex: Jenny runs 95 meters in 15 seconds. Find her average speed. Show all work. ____________ units are made up 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? v i = ____________ speed = v f = ____________ speed =  This equation is NOT in your PRT. You must _____________________.

Word problem hints: 1/ If an object starts from rest: v i = 2/ If an object comes to rest: v f = 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: mcm/s km/h mi 1/sft/s inm/s 2 mphkmin/ym/s cmhskm/h

III. velocity v = _________________________________ mag. of the velocity = the ____________ Ex: = ________________________________ __________________________________ velocity = ___________ + ________________ Draw velocity as an _________: =

average velocity: Ex: Godzilla moves 5.0 x 10 2 meters east in 2.0 seconds. Find his average velocity. If you assume that east is positive, you may write 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 v 2) 3) Why is the average speed over the entire time closer to the answer for part _____ ? d = the _____________ distance

Now find the average velocities for each part of the previous example. 1) v= d/t v v 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, there is___________________. And because: velocity = + changing either _____________ or ______________ or _________ results in acceleration. In this section, 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 = _________ gained each _________

Because a = _________, the ________________ of a is the same as the __________________ of the ________________in v:  v = v f - v i.  v = Since  v ____ 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 = Since  v ____ 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 given by the direction of the ____________ in the ______________, which may or may not be the same as the direction of the ________________.

a = 2.0 m/s 2, 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 moving at a speed of 21 m/s, that accelerates at 5.0 m/s 2 for 2.0 s? If it remains at this final speed, how long will it take 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 v i or v f 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) Find the average speed in the 0-5 s interval. Repeat for 5-10 s and 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? 12

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 a = 0 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 ________ d in each________________ dashed lines are__________ ________speed v i = ___  __________________

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

cart paper 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 at right. d (m) t (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. AB C Find v avg, d, and a in regions A, B and C. t (s) v (m/s)