Physics 3A: 1-D Motion. Physics 3A: 1-D Motion. Physics 3A: 1-D Motion. Physics 3A: 1-D Motion. What are the dimensions of v?
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1 i Physics 3A: -D Moion Kinemaics sudy of he moion of objecs, wihou concern abou wha causes ha moion. Dynamics sudy of relaion beween moion and is causes. Sar wih one dimensional (sraigh-line) moion Aerage Velociy Consider he moion of he car in he following: Posiions of he Car a Various Times Posiion (s) (m) A 3 B 5 C 38 D 3 E 4-37 F 5-53 Shoup 33 Physics 3A: -D Moion We define he aerage speed (scalar) as: d (.) where d is he disance raeled and is he ime ineral during he moemen. We define he aerage elociy (ecor) as "displacemen ecor diided by he change in ime" f (.) noe ha d depends on pah, bu and hus does no! f i i Shoup 34 Physics 3A: -D Moion Wha are he dimensions of? Wha are he unis of in SI sysem? lengh ime m s L T Physics 3A: -D Moion Ploing he car's daa gies us: Slope beween o poins on his graph gies us he aerage elociy (), for eample beween A & B: 5 m 3 m s s. m s rise run How do you specify he direcion of in -D moion? wih plus or minus sign. In addiion, oal displacemen is he "area under he cure" of a elociy ersus ime graph: (Do Eample.) n n n n n if ( > ) hen is posiie, if ( < ) hen is negaie. Shoup 35 n n n n n Shoup 36
2 Physics 3A: -D Moion Wha if we wan o know an objecs elociy a an eac ime? compue objec's "insananeous elociy" Insananeous elociy () he elociy of an objec a a specific insan of ime. Consider: Take he i: In calculus: d d (.3) Shoup 37 Physics 3A: -D Moion Summaror consan elociy, -D: Displacemen (ecor): Aerage elociy (ecor): Insananeous elociy (ecor): Speed (scalar): Model for consan elociy: d seing i f d d i i Shoup 38 Physics 3A: -D Moion Wha if he elocis no consan? => Acceleraion! Physics 3A: -D Moion Jus like insananeous elociy, we can define insananeous acceleraion which is he acceleraion a one insan in ime: We define aerage acceleraion as he"ime-rae-of-change" of elociy, aeraged oer some ime ineral: d d (.6) f i (.5) Properies of acceleraion: Since is a deriaie of elociy wr ime, graphicalls he slope of a elociy ersus ime plo a any poin: Wha are he dimensions of acceleraion? [a] = lengh / ime Measures how rapidly he elocis changing, i.e. a = m/s means elocis changing m/s in each second Shoup 39 Velociy (m/s) Slope => acceleraion Time (s) Shoup 4
3 Physics 3A: -D Moion Properies of acceleraion (con): Can also obain acceleraion from displacemen ecor: d d d d d d d d Physics 3A: -D Moion Properies of acceleraion (con): Acceleraion is a "change in elociy per uni ime" bu elociy has boh magniude and direcion, so: change in elociy's magniude ==> acceleraion! change in elociy's direcion ==> acceleraion! or boh! Mach he graphs: Consider consan acceleraion: slope = (a) (b) (c) consan ( f = ; i =) f i (d) (e) (f) (.8) slope = Wha is mean by "de-acceleraion? Shoup 4 Shoup 4 Physics 3A: -D Moion Physics 3A: -D Moion Anoher equaion comes from ersus plo, and ha area under cure is displacemen: area square area riangle slope = Now for posiion ersus ime: recall f i ( f = & i = ) bu so (.) (.9) Shoup 43 Shoup 44
4 Physics 3A: -D Moion Physics 3A: -D Moion Now pu in alue of acceleraion: Now we can pull ou alue of ime: a (.) f f parabola slope = (.) slope = Shoup 45 Shoup 46 Physics 3A: -D Moion Physics 3A: -D Moion Summary: Conains Equaion i f a X X X X X X X Shoup 47 Your Mission? => Problem soling:. Draw a picure (Model). Erac from "words" useful informaion 3. Decide on concep (i.e. consan acceleraion?) 4. selec equaion(s) which use info you hae and also info you wan. 5. Sole for unknown. 6. Adjus for significan figures and include unis! Eample of consan acceleraion ==> Free-fall Moion We all know ha objecs released near earh fall freely oward earh's cener. Due o graiy (see laer lecures) free-falling objecs undergo a consan acceleraion (ecor), poined oward earh's cener wih magniude: g 9.8m s 3 f s a y Shoup 48
5 Physics 3A: -D Moion Physics 3A: -D Moion B A C D E Wha's happening? A.?, a? >, a= -g B.?, a? >, b < a C.?, a? = D.?, a? = - a E.?, a? <, e > d F.?, a? f > e Conering our consan acceleraion equaions for free-fall moion gies: y g g g Wih g = 9.8 m/s or 3 f/s F Shoup 49 Shoup 5
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