Linear Motion I Physics

Transcription

1 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 graph of isance an ime Unis The Sanar Unis use in mechanics are meers an secons Displacemen versus Disance - Displacemen an isance are boh measures of how far an objec has ravele. - Disance consiers he oal pah ha an objec ravels. - Displacemen only consiers he ifference from an objecs iniial posiion o is final posiion (isplacemen is he shores pah beween he saring posiion an he final posiion) Example: y 2m Disance = 4m Displacemen = 4m x - Displacemen is ofen measure along each axis, an expresse as Δx an Δy. x = x f x i y = y f y i - Displacemen can be negaive, posiive, or zero Q1) An objec sars a he origin an ravels in he irecion of he posiive x-axis for 6 meers. I sops briefly, an hen ravels in he opposie irecion for 2.4 meers. Wha is he oal isance ravele by he objec? Wha is is isplacemen? 1

2 Q2) An objec sars a he origin an ravels in he irecion of he posiive y-axis for 4.5 meers. I sops briefly, an hen ravels in he opposie irecion for 6 meers. Wha is he oal isance ravele by he objec? Wha is is isplacemen? Q3) An objec sars a he origin an ravels in he irecion of he posiive x-axis for 3 meers. I hen ravels 6 meers in he posiive y-irecion, as shown in he iagram. Wha is he oal isance ravele by he objec? Wha is is isplacemen? y 6m 3m x We will use isance an isplacemen in physics. I is imporan o unersan he ifference beween he wo. Linear Moion Case 1: When Objecs move a Consan Spee - Moion moving in a sraigh line is calle moion - Spee is relae by wo variables, which are an. Q4) Two suens simulaneously run for 20 secons. If suen-a ravels 30 meers, an suen- B ravels 50 meers, hen which suen was running a a higher spee? Q5) Two suens boh run a isance of 50 meers. If suen-a reaches 50 meers in 10secons, an suen-b reaches 50 meers in 15 secons, which suen was running a a higher spee? Spee - Spee is efine as Spee = 2

3 - The symbols use ofen in physics are he following spee = ( ), isance = ( ), ime = ( ) The unis for spee are: Velociy - Velociy is closely relae o spee, bu as he propery of. Velociy = - For an objec o have consan velociy, i mus have consan an consan. Q6) Does a car going aroun a curve a 20 m/s have consan spee? Consan velociy? Graphical Analysis of isance vs ime: graphs of consan velociy Algebra review: The slope-inercep form of a line is: If he line passes hrough he origin (y-inercep is ), he form becomes: The slope of a horizonal line is. - The graph for funcion y=mx is shown on righ. - m is he slope of he graph an represens he raio of change in he y-coorinae o he corresponing change in he x-coorinae. - A larger slope implies a greaer rae of change - Here, y an x are jus variables which can be anyhing (such as isplacemen an ime) y m=slope x - If we rearrange v= / o =v, an raw isplacemen vs ime graph, hen he velociy v represens he slope of he graph - A seeper slope means greaer rae of change. Hence, he change in isance per ime, greaer velociy - Slope is linear. Hence, he velociy v is consan. v =slope 3

4 Pracice Quesions: Use v= / o solve he quesions, where v=velociy, =isance & =ime 1. A boy runs a isance of 10 meers in 2 secons. Wha is he boy s velociy? (a) 2m/s (b) 5m/s (c) 9m/s () 13m/s 2. A car ravels a isance of 400 meers in 20 secons. Wha is he velociy of he car? (a) 6m/s (b) 12m/s (c) 16m/s () 20m/s 3. If you run a a consan velociy of 5m/s for 5 secons, how many meers i you cover? a) 25m (b) 16m (c) 12m () 3m 4. A boa is moving a a consan spee of 10 m/s. How long will i ake o move 1km? (1km=1000m) (a) 120sec (b) 100sec (c) 75sec () 50sec *~ Use v= / o solve he quesions, where v=spee, =isance & =ime 5. An animal is walking a a consan velociy of 2m/s. How long will i ake o move 20 meers. (a) 10sec (b) 13sec (c) 18sec () 23sec 6. Which graph represens he greaes velociy? Why a) b) c) ) 4

5 7. The graph on he righ represens he moion of car. The car sars a he origin an sops a posiion C. A B i) When oes he car say moionless? a) OA b) AB c) BC O C ii) When oes he car have he highes spee? a) OA b) AB c) BC iii) Does he car reverse irecion? Yes or no. If yes, where? Frame of Reference The moion of a boy can only be escribe relaive o somehing else. The moion of an objec coul be escribe in reference o: - anoher objec - a saionary observer - a moving observer - a coorinae sysem Selecing he reference efines your frame of reference. For example: If you are saning sill on he siewalk an a car passes by a 25 m/s (abou 55 mph), he car appears o move away from you a 25 m/s relaive o your posiion (on he moionless groun). However, if you are also in a car going he same irecion, bu a 20 m/s, he oher car appears o move away from you a only 5 m/s. 20 m/s 25 m/s Q7) You are on he rain from Washingon DC o Philaelphia an he rain is moving a consan spee of 160 km/h (abou 100 mi/h). You have a ennis ball ha you oss sraigh up. i) To an observer on he groun, how fas is he ball moving? ii) From your poin of view, how fas is he ball moving? 5

6 Relaive Velociy Relaive velociy escribes he velociy ifference of objecs ha are in moion. The frame of reference is locae in one of he objecs. For objecs, raveling on he same sraigh line: 1.) If he objecs are moving in he same irecion, he relaive velociy is he ifference beween heir wo iniviual velociies. v1 v2 v r = v 2 v 1 2.) If he objecs are moving in opposie irecions, he relaive velociy is sill he ifference of heir iniviual velociies. Recall hough, ha objec one in he example below woul have a negaive velociy. v1 v2 v r = v 2 v 1 Pracice Quesion: 8. Two sun pilos are flying heir planes irecly away from each oher. Plane 1 is being piloe a a groun spee of 480 km/hr an plane 2 is moving a a spee of 500 km/hr. From he perspecive of he pilo in plane 1, how fas is his plan moving away from plane 2? 6