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Name: Unit 1: Introduction to Physics & One Dimensional Kinematics Big Idea I: Objects and systems havc properties such as mass and chargc. Systems ma)' have internal structure. Essential Kuowledge I.A.!: A system is an object or a collection of objccts. Objects are treated as having no intcrnal structure, a. A collection of particles in which internal interactions change little or not at all, or in which changes in these interactions are irrelevant thc question addresscd, can be treated as an obiect. Hi!! Idea 3: The interactions of an obiect with other obiects Essential Knowledge 3.A.I: An observer in a particular reference frame can describe the motion of an object using such quautitics as position, displacement, distance, velocity, speed, and acceleration. a. Displacement, velocity, and acceleration are all vector quantities. b. Displacement is change in position. Velocity is the rate of change of position with time. Acceleration is the rate of change of velocity with time. Changes in each property are expressed by subtracting initial values from final valucs c. A choice of reference frame determines the direction and the magnitude of each of these quantities. to can be described bv forces. Learning Objective (3.A.I.1): The student is able to express the motion of an object using narrativc. mathematical, and graphical representations. [Science Practices 1.5, 2.1, and 2.21 Learning Objective (3.A.1.2): The student is able to design an experimental invcstigation of the motion of an obiect. [Science Practice 4.21 Learning Ohjective (3.A.1.3): Thc student is able to analyze experimental data describing the motion of an objcct and is able to express the results of the analysis using narrative, mathematical, and graphical representations. [Science Practice 5,11 Hi!! Idea 4: Interactions between systems C'lI1result in c1ulIl!!es in those systems. Essential Knowledge 4.A.!: The linear Learning Objective (4.A. 1.1): The student is able to use representations of the centcr of motion of a system can be described by the displacement. velocity, and mass of an isolated two-object system to analyze the accelcration of its center of mass. motion of the system qualitatively and semiquantitatively. IScience Practices 1.2, 1.4, 2.3, and 6.41 Essential Knowledge 4.A.2: Thc Lcaming Objective (4.A.2.!): The student is able to make prcdictions abont the motion of acceleration is equal to the rate of change of velocity with time, and velocity is a system based on the fi'Ct that acceleration is equal to thc changc in velocity per unit time, and velocity is equal to the equal to the rate of change of position with time. change in position per unit time. [Science Practice 6.4] a. The acceleration of the center of mass of a systcm is directly propol1ional to the Learning Objective (4.A.2.3): net force cxcrted on it by all objects Thc student is able to crcate mathematical models and interacting with the system and invcrsely analyzc graphical relationships for acceleration, velocity, proportional to the mass of the system. and position of thc center of mass of a systcm and use them to calculate properties of the motion of the center of mass ofa svstem."rSciencc Practices 1.4 and 2.21 _ Proficicnt Reading assignment Read Chapter Section 1.11. 1 and 2 then answer Motion: the following questions: A First look Define the following terms: motion diagramIn a motion diagram what do the following things indicate: equally spaced images ___________ , increasing the distance between images . ,decreasing the distance between images _ particle model - Answer the "STOP TO THINK 1.1" question near the bottom of page 4 - now, stop and think about the answer to this question, then flip to page 27 to check the correct answer! Answer the "STOP TO THINK 1.2" question - make sure you take time to engage yourself in the ideas! 2. Use the particle model to show a motion diagram of a car speeding up as it moves to from ieft to right across the rectangle below. Use 7 dots, making your diagram go all the way across the rectangle. Section 1.2 - Position and Time: Putting Numbers on Nature 3. Define the following terms: position origin Displacement- 4. Explain what is meant by the time referred to as t = 0: S. How is displacement calculated? 6. STOP TO THINK 1.3 - Provide 2 examples that show why the correct answer to this question is C : Section 1.3 - Velocity 7. Define the following terms: Uniform Motion Speed Velocity - 8. How is speed different from velocity? Reading assignment Answer the "STOP TO THINK 1.4" question Section 1.4 - A Sense of Scale: Significant Figures, Scientific Notation, and Units 9. Why do scientist use significant 10. What is precision? figures (what does it tell them about a measurement)? Why is it important in taking data? Answer the "STOP TO THINK 1.5" question on Page 16 Section 2.1- Describing Motion: 11. A motion diagram is a basic picture of motion, why is a position versus time graph not a picture of motion? 12. What does a steep slope on a position versus time graph mean about the objects motion? 13. How can a velocity vs. time graph be created from a position versus time graph? 14. How can displacement be determined from a velocity vs. time graph? Answer the "STOP TO THINK 2.1" question on Page 33 Section 2.2 - Uniform Motion: 15. From a position vs. time graph how can you tell if the objects motion is uniform? 16. Why is the area under a velocity graph displacement? Answer the "STOP TO THINK 2.2" question on Page 35 Section 2.3 - Instantaneous Velcoity: 17. Define instantaneous 18. How can instantaneous 19. When is instantaneous velocity. velocity be determined from a graph of position versus time? velocity the same as the average velocity of an object? When is it different? 20. Using conceptual example 2.4 on page 37, write a story about the motion another object (other than a hockey player that exhibits the motion shown on the graph Reading assignment Answer the "STOP TO THINK 2.3" question on Page 38 Section 2.4 - Acceleration: 21. Define acceleration. 22. Using a motion diagram, how can determine 23. How can acceleration be determined 24. What does the sign of acceleration information about the acceleration of an object? from a graph of position versus time? mean in terms of whether 25. Can an object have negative acceleration an object is speeding up or slowing down? and be speeding up? Answer the "STOP TO THINK 2.S" question on Page 41 Section 2.5 - Motion with Constant Acceleration: 26. What are the three constant acceleration equations? 27. What is the significance of the Y, at' in the position equation? Where does this come from? Answer the "STOP TO THINK 2.6" question on Page 45 Section 2.6 - Solving One-Dimensional Motion Problems: 28. Describe the steps in problem solving strategy. Read through example problems to see how the book using the strategy. Section 2.7 - Free Fall: 29. Define free fall 30. Explain why in the absence of air resistance, two objects of significantly different mass will hit the ground at the same time 31. What is the value for the acceleration due to gravity on the earth's surface? the book says are worthy to note about free fall. List some important points that Graphing Motion Homework Problems (answers on last page) A. Description: x Two cars travel on the parallel lanes of Car I a two-lane road. The cars' motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters. 1. At which of the times do the two cars pass each other? How do you know? t) ..,S~ p\o.( t. eM- 'l>~ ~ rw C.ar 2. Are the two cars traveling in the same direction when they pass each other? Explain! tJb, Cctr 2. 'M~ t--) S\op( et (g.r _1 1 \-ID.~ 3. At which of the lettered times, if any, does car 111 momentarily stop? How do you know? :n. d~sn '+, L~r '1 hoJ vtloti~(-tv\''( e.V\\1rt (OY\Sr-~-t. 4. At which of the lettered times, if any, does car 112momentarily c..1W.("~ \') ~\Ot>-e lLt C t'O -\1(V'4 ') stop? How do you know? ,,=O~) lS\op!. i••~~r1) "'0 5. At which of the lettered times are the cars moving with nearly identical velocity? How do you know? A- ~ o..n. (>o.xo-\\<,\ tIN') s\ 'il0 ~ B. You are running in a race (I'm impressed!) and we have decided to graph your movement. e.o-r 1.~ 1. u.-a. :l~S 6j Displacement 1800 1600 running L What time '/-=2. in those first 90 seconds. is your average period (a-90s)? YSO-Q.. 'to-o velocity "2 ?C> 0 _10 _ Are your answers different? '"'" 4. .;"'" - '" 1000 ~ 800 o ,Ill:;' H' •• 0" '1";": ~~',1'~t:. )! Po-: 'I~ ,~ "~ o..r RI>" !LiT ~,!, ' " i::'"::; ,\., ;;:",: :':;" ,'t! ;.::.,1-:. ~.. ;y,, ;~ '~'- ~-, . "~ :~r 'e~!;--: o f:~ m. ii '". ,,~. ;p.~ ~~:''', 60 .i" ,,!i.' 120 ~.f;.~ 180 1'7, - 1'":.>1 240 ,. h v<,1t> cAhj and now you're out of breath! ./ .. / A 1z: ?~ '" / '/1. :'1 ..... ; I '/ .. - , >-, ~'., ,-- 300 Time(s) period? ]f lc), 5 this time ,!",,; "If, :'IF !~: • h :, •••• '';=,.. 7~i~ ... ',~ 1!;ii :;;~ .. , i'.;~ ,. ~~ . rj~.'!:' ~ ~ 3!., " ;:"'1 600 Jr.1" "";.(.~' :-"--w .,' :i::ij1~P,t~ .. ~i .. ~ ~~;.;1-1 400 mj i:j~~;r,; .. , :.:: .•.. :;1~ :~~ o Z 0... (OV\& \-Wl t- during ;;;; :'~~; ,. ... I':,ri ':'r..l :'!~,' ~ --or, ~'".':i ';., ::l~r, 'il'j;. Are you accelerating? What is your distance ~ ,"Ii; il. ::.~,I]::i: ~"l j:'!' 200 at 60 5. Nt>. 90s to 1505 Yikes! You ran too fast at the start 6. E ,~ to 1 and 2 the same or Why? f'l\ov \ Y\ ~ ~ 1200 .!!? velocity _ 1400 '" a. oS . V ~ -\#0- 0 3. this =tC;~ j What is your instantaneous seconds? during E := c: vs Time {!;I :I;; :,!' ,. , ."., I\' ., . -, i;~~ '"i' .,.~', " .~ . // /' ;;,~:~yii1i7 ., , f" "n ~r~ 'tn<+ . . .. "....:. , , ? -, ;:~:'Wi ~~''I, ,",' ;;;;1 ':,~' ;,," ," '/ .~ -;v:: ~:.~~ffi~ (:~ ~~' Zero to 90s: Let's look at how you are ~,S(1...l"Y'II.. 360 420 480 54' Graphing Motion Homework Problems (answers on last page) What is your velocity during this time period? 7. O~~ What happened? 8. o\-<rp~, 150s toQ: By looking at the graph are you moving lfaster 9. or __ l';)\-~ 10. What is your velocity during this time peri~d? V -= 2405 to 300s \0100- 4&St> :: ~()O - ~ '2..110 - 1St) OJt> - 'J-= ~C5c- \0$'0 ~~ - '2.&.tt:> :. -_'2.00 L' S\~~ J l# ~ @i1 -:..o~ What is your velocity in this period? 11. slower than you did in the first 90 seconds? ~ -: CD C 12. What does Uils mean (which way are you going.) bo..tf ~()..f"ds Ceo Of" Or'ijh'''(Mt>,jf\~ o\\(t~M.), ~~Jt \'\ 3005 to 360s 13. How would you describe your motion during this time interval? V\0t- Movi~lStor~). '1>\~ '"D. 3605 to 5105: You know that you have only one chance to still win the race... run as fast as you can! flO. 3 ~ J 'l_ @ -= =,=,0 ~ 11.~~ 14. What is your average velocity during this time period? V~ 15. \~OO-\000, SLfo - -= 'b'1o (Y) a. What is your instantaneous velocity at 420 s? b. What is your instantaneous velocity at 480 s? 000 lqc!)O .\f -= 1 (*1.\1.0) . 42e - .Bo Cio '-J ::. 11,,00- (o..\"""4~'.> S\O - (000 ~,\D _ \000 I2-D 16. What do the differences in 14 & 15 represent? (what does a curved line on a position vs time graph mean?) \H\o(,i~ is if\cr.faSw4' We (}x..( sp-uc;l;J lAf' Now Construct a Velocity-Time (v-t) Graph for your motion You need to remember that the rules for dot graphs do not apply to v-t graphs. A common mistake is to assume that all three types of graphs work the exact same way. The graphs can be related to each other, but that doesn't mean you look at them the same way. Note: A straight sloped line on a v-t graph means acceleration. The slope of the line is ~qual to the acceleration; a positive slope is a positive acceleration, and a negative slope is a negative acceleration. There is one other trick you need to know about v-t graphs. If you multiply velocity by time, what do you get? Displacement, since d • = vt ! So, if I have a v-t graph and J calculate the area under the line (which means I'm calculating velocity X time). I will know how far the object has gone. Graphing Motion Homework Problems (answers on last page) 17. Graph your velocity vs. time on the grid below. label your axis with proper units and use an appropriate scale for both time and velo~ity. : / rT / .. - , if I I 1- s -f--C - - 1-- .- -- - - - I- - I - -- I J I / , I 0 60 120 180 2\10 3 360 420 4~O 540 I -r 1-'--- 1- -1= -t- f- -s I -- : I , 18. In the table below properly identify the type of velocity you exhibited during the race Time interval Canstant ar Changing +, -, zero Average Velacity (m/s) Ave. Acceleratian (m/s') Zero to 90s eMS\-o.nJr -r 90s ta 1505 (J>\I\~to.nt t~rb 150 ta 2405 toy\"oTvV'~ -t 240 ta 3005 c..t)Y'\S>~ ~ 300 ta 3605 Ct> n.'t.\o..v\k" re~t> 360 ta 5105 c...,",,-~i~ -t ""5 0 0 +<1.(, 0 0 -~.?; 0 0 0 S:~ ..• + .0\115 AV ()..--- 6\- n"\ ~1. Graphing Motion - Velocity vs. Time graph (answers on last page) SHOW All WORK IN SPACESBelOW Modified from J. Kova/cin 9/17/01 C. The following graph describes the velocity of an automobile as a function of time 30 ~J f-\(J! 'il 1. What was the velocity of this c t = 3S SeCOndS?~ -:: 2. During which time interval/intervals car at rest? How do you know? eM \ S ~ ~ ~ 6 was the ~ Pt~ r.t!.\- \It \ 0 c.i hj i~ ~~ ()J.;\ 4. What was the displacement t>.rto.. s o rY\ (Mt T ~ 0 III "OJ At> -= "' \00;-1'5t> blC 35 -\ 50 -t?, 60 0 90 -.1$ 0 ,I I I I , \ I " U III I .> I ~ ~ ~ ~ W ~ W T!MEfscc) ~ (\0 Y-'n) ",. ~ _ 100 II01W - -l( \0 i- L.D] = it~.o \)1 ~\\Ob~\ vt\oci ~ is l:,-trl». of this car between t = 25 and t = 40 seconds? -t (-'2.1..<;) of this car between t = \"-1\ '2..5 ~cl4l + Lt'50 + 1<100+11'2...5 yY\ 1 = 0 and t = 110 seconds? t iY\(.\v..O.~ 10r OfI.()J -l' I 4 - '). =1+\I5Dm \ = 0 and t = 110 seconds? (is it different (~-t <: -) from 117 and why?) +~,.~ =~ of the car and graph scale the gra~: ()\~fe at -'2. I of this car between t = 10 and t = 25 seconds? the data making sure to appropriately Time Acceleration (s) (m/s') S 20 ~ I 10 e.~ 'i,..Q5~ 9. Calculate the acceleration I I ~ I \'So •. l.t'SO + 11;00- \\'2..; - 1>"1,1; ~. I ,/1 -10 8. What was the total distance traveled by this car between t A\l , - V of this car between t = 0 and t = 10 seconds? 7. What was the total displacement +\00 10 ~ I L'oy.n') ': ~ ( V~,C\?)= A'('flo..~ctw . 't+J( '),0' "eo YV\.ovi""3 6. What was the displacement At.-=: ~ II 'ptLCUA.-I. ~ \).W\6-~ -\oWO.~N~: 5. What was the displacement 20 I •••• ..., -30 3. During which interval/intervals was the car moving in reverse? How do you know? 2" ~ q 1.\; 1-' -20 \Q~ ~'2.SS{'C-tro). 'c7e\-V"-t.(,n I I 'I b-? P ::-lID v~.l) I I 3 I ~ :!\ ,....~( ~. 0 t I '" '1. ~~ II) 20 30 4IJ ~ 60 ~ IlO 90 lJME(=J, 100 110 120 1-0 Problem Solving "0-= o~ Levell problems: 1. A car is at rest on a horizontal surface. The accelerator is applied and the car accelerates at 3.00 m/s': a. What;iiibe the speed of this car after 6.50 seconds? ,,-= (1::::y~... ;-~--l =~~~-. 1" (j,) lID.'!» b. What will be the average speed of this car during thes \:;-0.(,.5$ VA.'"':: \I-:;? c. t,=Vin s q.i'it e"S -= (tj;:: .,.1S) q.1S ~ :>. i. -t g",~'2.. -tC~)("',s)'Z..:- tl3.LtM. A ball is dropped from the top of a building to the ground below. It takes 2.87 seconds for this ball to reach the ground; a. What will be the velocity of this ball as it reaches the ground? V,:: = ~o=0 ~ 3 (,."3.'"\-0 0 seconds? How far will this car move d ring these 6.50 seconds? )(~ 2. =- -',ttl tf-b )if '/..-::'Jf -to ~ 13 -: "= t> \10 l' q.. ~ v. ~ tj-i: U :ti~. t~. \~J ~t. = ~ r;~ ~q.~)(1.."i') b. What is the average velocity of the I:lal as It ralls V,."( ""-2 S. ~ c. 0 -: Of" 0 he ground? l-/O.l/ V4)/(= How tall is the building? h= iC3t2. = -0 :~ 1..~1 ~ 1 .J. (1.~){'2.~1)'2. :> \40 .•.• 1\"\ m) 'l. l. _ ..... . __---1 3. A ball is thrown upward so that it just barely reac es the top of a telephone pole and then falls back to 6~-::;.2 the ground. The time from the release of the ball until its return to the ground is measured to be 5.20 ~ -: ". ~~ -0 '" 2.l,., 5 ':0 • I XD+ Vo\: '::' tI ~ 'Z. -to 2.~,. 0 .• i. ('I.V) '7.. 1#) :. r3~.\ ~ ~.g'~... V2.oe t 21A./)'I- \/0'2. 5. e -:. (J'Ot .• 2("l.~(6)t.) V'L::. I'iLlI.J . oJ 2~'11.2. -::) f-:. 38. m/s. \V= ~W3C;.1. 0 f\'"\ 4. A ball is thrown downward from the top of a building 122 meters tall with an initial speed of W\ What will be the velocity of this ball as it reaches the ground? .~'IC~-::\'2.2.ltliVeI2 problems: _ )l 'Z. '6 \.10: t"'ll""W' -:: ~ ~ V,;? '/.. - seconds. What is the height of the telephone pole? ".:. 0 ] v\."7 . ~---- Suppose that a car is moving with a speed of 18.5 m/s when the brakes are applied so as to slow the car down at a rate of -2.85 m/s'; to a. What will be the speed of this car 3.55 seconds after the brakes are a . d? Vo- \~.S 5 4\.:-Z.?~~ b. = V-= Vo-t'Clt ~~ Ig.S t(-2..~SJ(3.S5) ': ~.J.ttY'o/S far will this car move during this 3.55 second period? b~ -= )(0 l--+1.. ~ +VO-\:-t 0 4{\'l.,)('3~'5)+ iG'l.'~I:;)(3.~S) c.bSJolt\I !DOg will it take for this car to stoP'-" V =Vo + 11\..lc d. H~ -:!) ':l. W~ 0 '= \<l.S~ (-'2..75)~ V':: 0 u=: \ - 1:l.L..1l'Y' - ':!J 1;= -I~.S :-2..••. S't: _ -1'1'.!O -:~.5'sJ -'2..,•••• will this car move from the time that the brakes are applied until the car comes to a stop? - 6 y.. -:::. ~ \ t V" tT 01 ~ 'l.- "Z. 0.- ':a.. -:::C!~.Gx.c..S)of i(-2.'iS)(~.5) -::: \"2.0.'2.') + -l,pO.'2. ---.. \b)C. -:.1ot)l'V\ \ 1. .,7Vo of: V:: 0 1,Q.bY. + 1.[-1.. , ••) A)(. ;,r&. ~'.f l'll.1.~ = b)(. c,), -: lo~ 1-D Problem Solving - l&.f4tf _)( -''l.tt - 'l'f- -= -'2.•.•0 .f 1?l# 1 +'2.Yc.-=f3"\~.lI"Y'\J 1~.111 1-0 Problem Solving Suppose that instead of throwing this ball upward it is thrown downward with a speed of 38.0 m/s; g. How long will it take for the ball to reach the ound? t:: 4.IS '1.-=)!.""dt-~~~t'L O~-z.4.""~f1t1".I.~V)t"Z. h. What will be the speed oTthe ball as it reaches the ground? \I( "1.= "f>.•..to ~o..6'f. -= ~~ -tU1.i)(Zqo) :: ~l-~"'~ J 9. A car is initially traveling with a constant ve oClty of 12 m/s as it moves down the highway. The car travels _ \'J,.~a distance of 175 m at this velocity. ~How long will it take the carto travel th~75 m while moving at a constant 12 m/s? 0..~O~ ble "0' ., '#.~\"~ 'It,: ~:--tl) "). ~o .•..vo"", ~ 111'-=O+ll'2)t ..•.~D1: !J!::-t 1"2. :tB.(,~J ('O:6ro..-.t-ve\otilv. 'J -- b. After moving at lL m/s for the time found in part a, the driver pushes her foot down farther on the gas ~edal, accelerating at 1.5 mis' for 10 seconds. i. How fast was the car moving after 10 seco a elerating? .•.V; 1.'1(). ~ " -:: VD + •.• ~~\'l o.."'c ,,:: '; l'2.t(I.~)l\o) 2.1 t!) ~ ii. How far dia the'i:ar move during this )(:: ~D+'JOt+:!z...~'2. acceleration? 1" r)C- l'\S ':l. l - -:=o+I\'2.\t\o\+~(\oS)lIO) fY'\. " c. Just as the driver r~aches the spela found in part c. above, she notices an accident has occurred farther down the road and she applies the brakes, coming to a compl~p after traveling an additional 50 meters. i. What was the acceler~ion of the car while stopping? Ol. X \lole -+ ~~ 'to '.J1--; "'f;)'1.-., tp..l:.)L / J,00 -= }-z.1 -= ;0 ~h..,)(-t)+=io..-t'Z tl'\O''t-~ 1> ~ 2"1'1.. ii. How I~ng diOit take fOr the car to stop? ~O = '2.1 (~) +:l (-1"'1')~-z. Of" V e Vo -t 'ii I'" "'-'.'1-'1 l!':loz.] ~ 2,.0..(150) i-Q..t '= 2.' •.t-,,7.."I)~ I 2.1 .: 2; ;" t = d. Make accurate graphs of position vs. time. and velocity vs. time on the axes below shliwlhg the motion of this car during this entire problem. V (mls) X(m) 500 30 400 24 300 18 200 12 100 6 t (s) t (5) o 5 10 15 20 25 30 o 5 10 15 20 25 30 I "3.1$. l-D Problem Solving _ \G.~ ~, St. OJ -\:: ~ ~~ 10. Santa's elves are building an experimental rocket powered sled. The rocket sled is mounted on wheels and placed on a set of straight railroad tracks. At t=o the rbcket is ignited, causing a constant acceleration of 15m/s2 until t= 8s. From t= 8s to t= 20s the rocket travels at a constant velocity. At t= 20s the engine is shut down and the brakes are applied. a. What is the velocity of the sled at t=8s? \ .'I ':.Vo ; tt.-t ':. 0 -to \st!) ':: 1'2.0 '!l ~ b. How far does the sled travel durin x= Vot .• to\t~ = ~ (15) (I).... seconds? -= {lifO rn \ fA":" 0 c. How far does the sled travel from t=8s to t=20s? ~-z.o-'t \:. 0;. \'l- lC -; Vo ~ V, t = -t io..t'2. ""~ X -::G'2.0')l \'2.) CAV\.\~+ 1/ -=0"1.\0'"" ] -t C> . . d. After the brakgs are applied at t=20s the sled continues to move forward for 680 m. Calculate the acceleration while the brakes are applied. _ -1'-1,#0 D X 0:: 'lot"," 'io....'c 1. (f\JI..ll.. '" '11.-;. "D7-.•.?-tA.b y. 0'('" MJ. ') 0 fA. - i((,?D = Q1.0)~ i' '2. 0..( CIVt» Q. -::-10.V? e. Calculate how long it takes the sled to come to a stop after the brakes are a V,. = V" -t O.:t t- -;.-=-10.\1 ''1b of" -= C ~ \ '2..0 "" (-Ib.~)-\:. f. Graph the motion of the sled from t=Os until it comes to a stop. 140 m/s ?500rll ,. - ,120m/s 2000m 100 m/s 1~OOrn- .. 1000m 80 n\ls , 60 m's . 40 m's • 20 m's .--t-~t--t-t--,t-+--i,-4 v 4 8 .. -t,-+-+,. 12 lG 20 24 .78 32 30 40 ,., I -I-f--t-I-t---i-l 4__ 8 _'2 _ Ie 20 '4 28 0' .. 32 3Ii 40 44 Answers to Graphing Problems and 1-0 kinematics Problems A. (two cars) 1) D (when positions are the same), 2) No (car 2 is going in the reverse direction), 3) Never (constant slope means constant velocity), 4) C (zero slope means zero velocity), 5) A (slopes are identical) ~t"cf>fHtl B. (you running a race) 1) 5 mis, 2) 5 mis, 3) slope is constant so velocity is constant, 4) No,S) 0, 6) 0, 7) Stopped 8) ~ 9) 6.7 mis, 10) -3.3 mis, 11) backwards (maybe your hat blew off and you ran to get it), 12) at rest, 13) 5.3 mis, 14) a) -4.2 mis, b) - ~m/s, 15) acceleration, 16) 17) 0-90: canst., +, 5 mis, a mis' a 90-150: const, 0, 0, 150-240: const., +, 6.7 mis, a 240 - 300: canst., -, -3.3 mis, mis' a mis' 300-360: canst, 0,0,0 mis, 0.07 mis' 360-510: changing, +, 5.3 C. 1) -10m/s 2)10-25, 45, 110- velocity is zero 3) 25-45s velocity is negative 4) 100m 5) 0, 6) -112.5m 7) 1150m 8) 1450m 9) -2, 0, -1.0, 3, 0, -0.75 mis' , , , , ,, , , , , I , , , J ,, , , I , 10 , , , ,, , , , , , I , ~ , I , , , I I , , , , , ,, , , I , , , , , , , , , , , , I , ,, , , ,, , ,,, , ,, ,, , , , , ,,,, ,, , , , , I I I I I w ~ ~ ~ ~ m ~ I 100 IW I~ l1ME (KG) 1-D Kinematic 1 a) 19.5 Problems: m/s b) 9.75 m/s c) 63.4 m 2 a) -28 m/s b)-14.1 m/s c) 40.4 m 3) 33.1 m 4) -62 m/s 5 a) 8.38 m/s b) 47.7 m c) 6.5 s d) 60 m 6 a) a b) -52 m/s c) 5.3s d) 138 m e) 14.3 m/s f) 33.2 m/s 7) same at -59 m/s 8 a) a b) 3.9 s c) 11.7 s d) 7 & 0.7 9) a) 14.6 s bi) 27 10) a) 120 s e) -77 m/s f) 314m g) 4.1s h) -78.4 m/s m/s bil) 195 m ci) -7.29 m/s2 cii) 3.7 s d) ."".~ f' \. 11)-,--.• mis, b) 480 m, c) 1440 m, d) -10.6 m/s2 e) 11.33 s f) "'~J '. - .. i I'''''' It " •• _. '."'. " z; rr.t "/ \ / I .. / to) ',-, "I -,D.C. 7~ ,..- . l' ~~ JOI