Linear Motion, Speed & Velocity

Transcription

1 Add Iporan Linear Moion, Speed & Velociy Page: 136 Linear Moion, Speed & Velociy NGSS Sandard: N/A MA Curriculu Fraework (2006): 1.1, 1.2 AP Phyic 1 Learning Objecive: 3.A.1.1, 3.A.1.3 Knowledge/Underanding Goal: underand er relaing o poiion, peed & velociy underand he difference beween peed and velociy Language Objecive: Underand and correcly ue he er poiion, diance, diplaceen, peed, and velociy. Accuraely decribe and apply he concep decribed in hi ecion uing appropriae acadeic language. Lab, Aciviie & Deonraion: Noe: Walk in he poiive and negaive direcion (wih poiive or negaive velociy). Walk and change direcion o how diance v. diplaceen. coördinae ye: a fraework for decribing an objec poiion (locaion), baed on i diance (in one or ore direcion) fro a pecifically-defined poin (he origin). (You hould reeber hee er fro ah.) direcion: which way an objec i oriened or oving wihin i coördinae ye. Noe ha direcion can be poiive or negaive. poiion (x): he locaion of an objec relaive o he origin (zero poin) of i coördinae ye. We will conider poiion o be a zero-dienional vecor, which ean i can be poiive or negaive wih repec o he choen coördinae ye. diance (d ): [calar] how far an objec ha oved.

2 Add Iporan Linear Moion, Speed & Velociy Page: 137 diplaceen ( d or x ): [vecor] how far an objec curren poiion i fro i aring poiion ( iniial poiion ). Diplaceen can be poiive or negaive (or zero), depending on he choen coördinae ye. rae: he change in a quaniy over a pecific period of ie. oion: when an objec poiion i changing over ie. peed: [calar] he rae a which an objec i oving a an inan in ie. Speed doe no depend on direcion, and i alway nonnegaive. velociy: (v ) [vecor] an objec diplaceen over a given period of ie. Becaue velociy i a vecor, i ha a direcion a well a a agniude. Velociy can be poiive, negaive, or zero. unifor oion: oion a a conan velociy (i.e., wih conan peed and direcion) An objec ha i oving ha a poiive peed, bu i velociy ay be poiive, negaive, or zero, depending on i poiion.

3 Add Iporan Linear Moion, Speed & Velociy Page: 138 Variable Ued o Decribe Linear Moion Variable Quaniy MKS Uni x poiion d, Δx diance d, x diplaceen h heigh v velociy v average velociy The average velociy of an objec i i diplaceen divided by he ie, or i change in poiion divided by he (change in) ie: d x xo Δx Δx v (Noe ha elaped ie i alway a difference ( ), hough we uually ue raher han a he variable.) We can ue calculu o urn v ino v by aking he lii a Δ approache zero: v Li 0 i.e., velociy i he fir derivaive of diplaceen wih repec o ie. We can rearrange hi forula o how ha diplaceen i average velociy ie ie: d v dx d Poiion i he objec aring poiion plu i diplaceen: x x d x v o where x * 0 ean poiion a ie = 0. Thi forula i ofen expreed a: x xo d v o * x o i pronounced x -zero or x -naugh.

4 Add Iporan Linear Moion, Speed & Velociy Page: 139 Noe ha i he lope of a graph of poiion (x ) v. ie ( ). Becaue v, hi ean ha he lope of a graph of poiion v. ie i equal o he velociy. In fac, on any graph, he quaniy you ge when you divide he quaniy on he x- axi by he quaniy on he y-axi i, by definiion, he lope. I.e., he lope i y y - axi, which ean he quaniy defined by will alway be he lope. x - axi Recall ha velociy i a vecor, which ean i can be poiive, negaive, or zero. On he graph below, he velociy i + 4 fro 0 o 2, zero fro 2 o 4, and 2 fro 4 o 8.

5 Add Iporan Linear Moion, Speed & Velociy Page: 140 Saple proble: Q: A car ravel 1200 in 60 econd. Wha i i average velociy? A: v v d Q: A peron walk 320 a an average velociy of How long did i ake? A: How long ean wha lengh of ie. d v I ook 256 econd for he peron o walk 320.