total distance cov ered time int erval v = average speed (m/s)

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1 Physics Suy Noes Lesson 4 Linear Moion 1 Change an Moion a. A propery common o eeryhing in he unierse is change. b. Change is so imporan ha he funamenal concep of ime woul be meaningless wihou i. c. Since changes are a resul of he moion of maerial, ofen a he submicroscopic leel, we sar suy physics wih a suy of moion.. The complex moions in our aily experience can be unersoo as combinaions of simple ones. So, we begin our iscussion of moion by rying o escribe an unersan he simples kin of moion. Moion is Relaie a. Moion occurs all aroun us, eiher isible or inisible. There are moions a microscopic leel such as josling aoms make hea an soun, flowing elecrons makes elecriciy, ibraing elecrons proucing elecromagneic waes. b. When we iscuss he moion of somehing, we iscuss is moion relaie o somehing else. c. Een hings ha appear o be a res, hey may moe a ery high spee relaie o he sun an sars. 3 Spee a. Two funamenal noaions space an ime are a he core of our concep of moion. b. Definiion: Disance coere per uni of ime. Spee is a measure of how fas somehing is moing. I is he rae a which isance is coere. c. Uni: Meers per secon (m/s) is he primary uni for spee. Ohers such as miles per hour (mi/h), kilomeer per hour (km/h), ligh-years per cenury are all legiimae unis for spee.. Aerage spee: aerage spee = oal isance co ere ime in eral = = slope =, = aerage spee (m/s) = oal isance coere (m) = ime ineral (s) e. Insananeous spee: The spee a any insance of an objec is calle he insananeous spee. The insananeous spee of a moing objec is equal o he slope of he angen line a ha momen. f. Consan spee: The spee a any insance of an objec is consan. slope of he angen 4 Velociy a. Definiion: Velociy is spee in a gien irecion. Velociy is how fas an in wha irecion i moes. Quaniies ha hae boh a size (or magniue) an a irecion are calle ecors. The spee is he magniue of elociy. Mr. Lin 1

2 Physics Suy Noes Lesson 4 Linear Moion b. Aerage elociy: aerage elociy = =, oal isplacemen ime ineral = aerage elociy (m/s) = oal isplacemen (m) = ime ineral (s) c. Displacemen is a ecor quaniy; is magniue is he sraigh-line isance beween he iniial an final locaions of he objec, an is irecion is from he iniial locaion o he final locaion.. Consan elociy: To hae a consan elociy requires boh consan spee an consan irecion. Moion a consan elociy is moion in a sraigh line a consan spee. 60 mi/h Eas 60 mi/h Wes Same Spee Differen Velociy e. Changing elociy: Eiher spee or irecion (or boh) is changing an hen he elociy is changing. Moion a consan spee can hae changing elociy all he ime when i moes along a cure pah. f. Car example: In a car here are hree conrols ha are use o change he elociy: he gas peal, he brake an he seering wheel. 5 Acceleraion a. Definiion: The rae a which he elociy is changing is calle acceleraion. I is a measure of how he elociy is changing wih respec o ime. b. Acceleraion: acceleraion = a = Δ change of elociy ime in eral, a = acceleraion (m/s ) Δ = change of elociy (m/s) = ime ineral (s) c. Consan acceleraion: The acceleraion a any insance of an objec is consan. In high school physics, we only eal wih consan acceleraion. a a = Δ = slope. Acceleraion is change: Acceleraion applies o changes in irecion as well as changes in spee, i.e., changes in he sae of moion. The acceleraion applies o increases as well as ecreases in spee. Someimes, he ecrease in spee is also calle eceleraion, or negaie acceleraion. e. Acceleraion is irecional: Acceleraion, like elociy, is irecional. If we change eiher spee or irecion, or boh, we change elociy an we accelerae. When linear (sraigh-line) moion is Mr. Lin

3 Physics Suy Noes Lesson 4 Linear Moion consiere, i is common o use spee an elociy inerchangeably an he acceleraion may be expresse as he rae a which spee changes. acceleraion (along a sraigh line) = change in spee ime in eral f. Car example: Cars haing goo acceleraion means being able o change elociy quickly an oes no necessarily refer o how fas somehing is moing. 6 Free Fall: How Fas a. Definiion: When here is no air resisance an he graiy is he only hing affecing a falling objec, such moion is calle free fall. Elapse ime: The elapse ime is he ime ha has elapse, or passe, since he beginning of he fall. b. Acceleraion ue o graiy (g): The free falling objec is experiencing acceleraion, i.e., a change in spee. The alue of acceleraion (g) is abou 10 m/s. More accuraely, g is 9.81 m/s. c. Insananeous spee: The insananeous spee of an objec falling from res insananeous spee = acceleraion x elapse ime or = g g = = slope = 0 m/s 3 s = 10 m/s s 4 s = 0 m/s 1 s 5 s. Iniial spee ( i ): Wheher he objec is moing upwar or ownwar an no maer wha he iniial spee i is, he acceleraion ue o graiy is always he same (9.81 m/s ) he enire ime. Tha means, uring each secon, he spee or elociy changes by 9.81 m/s ( 10 m/s). The final spee ( f ), he insananeous spee, is: f g = f = i + g = slope i = 30 m/s 0 s 6 s = 40 m/s 7 s 7 Free Fall: How Far a. Spee an isance: The spee an isance are ifferen. The insananeous spee an aerage spee are ifferen oo. The insananeous spee of 10 m/s a he en of 1 secon oes no mean ha he objec falls 10 m uring he firs secon. Bu, if he objec falls 10 m in he firs secon, he aerage spee of he objec is 10 m/s. b. Aerage spee: For any objec moing in linear moion wih consan acceleraion, he aerage spee is: iniial spee + final spee aerage spee = f or = i + f c. Disance-ime formula: Since a = Δ or f = i + g (1) i a = Δ = slope = i + f () Mr. Lin 3

4 Physics Suy Noes Lesson 4 Linear Moion =, or = (3) Subsiue () ino (3) an we ge: Subsiue (1) ino (4) an we ge: = = ( i + f ) (4) = ( + + g i i ) = i + 1 g. Free fall: Since i = 0, he isance-ime formula becomes = g = 1 g The falling isance of an objec is epens on ime square, so, he graph of he isance-erseime is a parabolic. If g = 10 m/s, he falling isance is shown in he able: Elapse Time (s) Disance Fallen (m) : : ½g e. Disance-Spee formula: Since f = i + g or g = f i (1) = i + 1 g () Subsiue (1) ino () an we ge: = i ( f i g )+ 1 g( f i g ) = ( i f i g = i f i i = f g )+ ( f i ) g + f i f + i g (3) Rearrange (3) an we ge: f = i + g 8 Graphs of Moion Mr. Lin 4

5 Physics Suy Noes Lesson 4 Linear Moion a. Velociy erse ime graph: Velociy (m/s) b. Displacemen erse ime graph: Displacemen (m/s) c. Acceleraion erse ime graph: Acceleraion (m/s ) Time (s) Time (s) Time (s) Time (s) Velociy (m/s) Acceleraion (m/s ) Displacemen (m) The slope of he elociy-ime graph is equal o he acceleraion. The area uner he elociyime graph is equal o he isplacemen. e. For a freely falling objec, he acceleraion erse ime is a consan, he spee erse ime is a irec proporion, an he isance erse ime is a parabola. f. Hang ime: When ahlees jump up in he air, he ime uraion hey say in he air is calle hang ime. 9 Summary of Formulas = f = i + g a = Δ = i + 1 g = i + f f = i + g Mr. Lin 5

6 Physics Suy Noes Lesson 4 Linear Moion 10 Air Resisance an Falling Objecs a. Air resisance causes he ifferences of falling beween feaher an coin. When he falling is ese in he acuum ube, boh of hem reach he groun a he same ime. 11 Linear Moion Example Problems For all he following problems, assume all he surfaces are fricionless an he air resisance can be neglece. The alue of g can be approximae o 10 m/s for simpliciy. a. James hrows a ennis ball upwar a 10 m/s, (a) how high will he ball reach? (b) How long will i ake for he ball o fall back o him? (c) Wha s he spee of he ball when i falls back? b. Mr. Lin is falling ino he ocean from a cliff of 1000-meer heigh, a) how long will i ake for Mr. Lin o reach he surface of waer? b) Wha is Mr. Lin s spee righ before he falls ino he waer? c. Bogy foun a hazar roa coniion 100-meer in fron of him. If his car is moing a 10 m/s, (a) wha s he minimum consan acceleraion require o aoi he anger? (b) How long will i ake for his car o be fully soppe uner such acceleraion?. Thomas s car moes a 0 m/s while Shalin s moes a 40 m/s. Boh cars are esigne o ecelerae a 5 m/s when he brakes are engage. a) Wha re he ski isances for boh cars? b) Compare heir spees an ski isances. Wha kin of conclusion can you raw? e. Anna is hrowing an objec upwar from he ege of a 10-meer all builing a 10 m/s an falls o he groun. (a) How long will i ake for he ball o hi he groun? (b) Wha s he spee of he ball before hiing he groun? f. If an oer-spee car is moing a consan spee of 40 m/s an passing a police car a res. If he police sars chasing while i passing an he police car can keep acceleraing a 4 m/s, (a) how long will i ake for he police o cach he oer-spee car? (b) How far will i ake for he police o reach he oer-spee car? (c) Wha s he insananeous spee of he police car when i caches he oer-spee car? Mr. Lin 6

7 Physics Suy Noes Lesson 4 Linear Moion g. Mary Jane freely falls from he op of a skyscraper of 550-meer heigh for 5 secons while Spierman is rying o rescue her. If Spierman jumps from he op of he same builing wih iniial spee ownwar, an he nees o cach her a leas 50 m aboe he groun o ensure her safey, a) wha is he minimum alue of require o finish his ask? b) Wha are he insananeous spees of Mary Jane an Spierman respeciely when hey mee each oher in he air? h. Vicoria slies own a 1000-meer long slope of 30 o freely from he op. a) How long will i ake for him o reach he boom of he slope? b) Wha s his spee when he reaches he boom? i. Ball A is freely falling from he op of he builing. Afer ball A falls for a meers, ball B sars falling freely from a cerain floor of he builing which is b meers below he op of he builing. If ball A an ball B boh reach he groun a he same ime, wha is he heigh of he builing in erms of a an b? Mr. Lin 7

Linear Motion I Physics

Linear Motion I Physics Linear Moion I Physics Objecives Describe he ifference beween isplacemen an isance Unersan he relaionship beween isance, velociy, an ime Describe he ifference beween velociy an spee Be able o inerpre a