Lecure 4 Moion nd Kinemics Reiew Turning Poins Inerpreing Moion Grphs Ls ime we lef off lking bou ccelerion nd urning poins. Recll ccelerion is wh chnges n iniil elociy o finl elociy. A chnge in elociy implies ccelerion. When ccelerion nd elociy poin in he sme direcion, n objec speeds up. When ccelerion nd elociy poin in he opposie direcion, n objec slows down. So now s reiew we ll spli he clss in wo nd he you pu moion digrms on he bord. A bll rolls up nd down n incline A bll ossed up which comes down long he sme ph f Δ - i Turning poin ccelerion Now h we re cler on ccelerion, we cn epnd our ides bou grphs. So fr we e looked elociy ersus ime grphs, bu now we ll look how posiion, elociy, nd ccelerion grphs rele. i f We e drwn he simples grph possible here. This moion would represen n objec wih consn posiion. Displcemen Δ= f - i is zero. Remember how he of elociy grph is ccelerion, i urns he of our posiion grph is elociy. = rise run = " " he unis of in his cse re m/s, unis of elociy!
So le s consider he elociy of his grph. Δ = 0 in his cse, so = 0. Now le s drw he elociy s. ime grph een hough i s riil. Accelerion grph is lso esy since here s no chnge in elociy (Δ = 0 =0) Now le s ry somehing lile more chllenging: [he someone wlk cross he room consn elociy] Le s drw elociy nd ccelerion grph o go wih his posiion grph. The of displcemen grph gies you ccelerion. = rise run = " " The here is consn nd posiie, so he elociy grph should be consn nd posiie. The of he elociy grph gies us ccelerion, in his cse ery esy. = rise run = " "
Since elociy is consn Δ = 0, herefore = 0. Before we moe ono oher emples, le s summrize: posiion " "# elociy " "# ccelerion Ne emple: [he suden wlk consn elociy from righ o lef] Moing in he negie -direcion consn elociy of posiion grph should be negie. Velociy grph is esy, consn bu negie. Since elociy is consn Δ = 0, = 0. Ne Emple: [he suden sr lue of negie nd wlk o he righ consn speed]
We he o sr our posiion grph negie lue, nd i hs o pss hrough =0 wih posiie. Velociy grph is esy consn posiie elociy. Accelerion gin is esy, = 0. Bu we should moe ono n emple wih non-zero ccelerion. We he n objec moing wih n incresing posiie elociy. Becuse he of he elociy grph is consn nd posiie, we cn drw he ccelerion grph ccordingly. The posiion is lile more chllenging. The of he posiion grph gies you he elociy. So we need o drw posiion grph h gies line wih posiie. I urns ou h prbol is good pproimion for wh we need. I mkes sense if we hink bou he fc h elociy is incresing in ech ime inerl we need o coer n incresing bi of disnce. The of prbol is line. The wy o describe prbol is: = 2 = = " " = 2 Noice h he of he posiion is line wih consn posiie. Now le s ry o mke moion digrm (simple his poin):
I hs posiie elociy, nd elociy is incresing, so we re coering more disnce oer ech ime inerl. To reiew bsic conceps concerning grphs nd moion: posiion " "# elociy " "# ccelerion The re of elociy grph gies you displcemen. The wy o find displcemen on posiion grph is o ke he difference in posiions: " = f # i One more bsic concep o coer, insnneous elociy nd ccelerion. The word insnneous implies h i hppens oer ery smll ime inerl. So le s do n emple. Wh s he insnneous elociy of his objec 5s? 5s We wn he elociy priculr momen, so we cn drw ngen line h poin o find he, hen you jus find he of h line. Th is how o find insnneous elociy from posiion grph or insnneous ccelerion from elociy grph. A couple of emples before moing on: A B A B 0 1 2 3 4 0 1 2 3 4
Do A nd B eer he he sme speed? If so, wh ime or imes? Eeryone ke couple of minues o wrie n nswer before we decide wh he righ nswers re.