x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions

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1 Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed Vector: Mgntude nd Drecton Poton, Dplcement, Velocty, Accelerton Don t Forget Unt! Coordnte Sytem Etblh the coordnte ytem ruler A number lne wth rrow howng pote drecton. Any drecton you chooe. The (or y0) locton dentfed. d Agn t cn be ny plce your chooe. Poton Etblh the coordnte ytem ruler Red the poton from the ruler Don t forget the unt nd drecton. Pote Poton Negte Poton Velocty Etblh the coordnte ytem ruler Velocty drecton pote n drecton of coordnte ytem. Velocty drecton cn lo be clculted from dplcement becue Pote Poton Negte Poton 1

2 Moton Dgrm Speclzed Dgrm tht nclude mot of the knemtc nformton. Ued tool to ole knemtc problem. Moton Dgrm templte re lble to prnt from the cl webte. Moton Type I Moton Type II Moton Type III Contnt or Speed up or Slow Contnt or Speed up or Slow Contnt or Speed up or Slow Prt I: Equton Prt II: Equton Prt III: Equton Crcle the known lue Crcle the known lue Crcle the known lue Problem Solng Proce Problem Decrpton: Th generlly gen. You mut dentfy n the text gen, the queton tht mut be nwered. Phyc Decrpton: Dgrm nd equton relent to the tuton. Soluton: The lgebr, grph, etc. And the nwer to the queton! Elutton: Check your unt, mgntude, drecton nd mtchng between repreentton.. Problem Decrpton Exmple A peron trelng left t 10 m/ for mn. How fr doe th peron trel? Phyc Decrpton Contnt 0 10 m/ 10 m/ 10 ec 0 0 A peron trelng left t 10 m/ for mn. How fr doe th peron trel? Contnt 0 10 m/ 10 m/ 10 ec 0 0 Soluton A peron trelng left t 10 m/ for mn. How fr doe th peron trel? m m 10 ( 10) 100 m

3 Elute A peron trelng left t 10 m/ for mn. How fr doe th peron trel? Unt Anly m m Mgntude 100 m bout 3/4 m Mut be rdng n ehcle Defnton of g. elocty Both de of equton re equl Mgntude Unt Drecton (t ector!) Velocty Mgntude Mgntude Unt Unt Drecton Drecton Rte of Chnge of Rte of Chnge of Poton Slope Re/Run Problem Decrpton Fnd the drecton (+/-) of the elocty n the tme nterl () 0 to 3 (b) 4 to 5 (c) 0 to 5 (d) to 4 (e) 3 to 4 Exmple All thee Velocte? Chnge n Velocty: lter elocty mnu erler elocty Aerge Velocty: Between ny tme If elocty ncree regulrly then fnd erge of nd f. Slope of trght lne between pont Intntneou Velocty Between tme jut bt fter/before t Slope of tngent lne t t Δ lter erler ( + ) f 3

4 Problem Decrpton Fnd the erge elocty n the tme nterl () 0 to 1 (b) 0 to 3 (c) 4 to 5 (d) 0 to 5 (e) to 4 (f) 3 to 4 Exmple Problem Decrpton Fnd the ntntneou elocty t the tme () (b) 3 (c) 0.5 Exmple Chngng Velocty Fndng the Aerge 1, 4, 7, 8, 9, 15, 35 1, 4, 7, 10, 13, 16, 19 4, 8, 1, 16, 0, 4, 8 Requlrly chngng elocty: Aerge the 1 t nd Lt The mddle lue Velocty ncree from 10 to 0 m/: g.? + f Cn you Identfy Intntneou nd Aerge Velocte? Fter nd Slower Speed? Defnton of ccelerton Both de of equton re equl Mgntude Unt Drecton (t ector!) Accelerton Δ Mgntude Mgntude Unt Unt Drecton Drecton Sgn cn get u Drecton Depend on Coordnte Sytem Choce Δ (+) - (+10) Δ -8 So ccel negte! 4

5 Accelerton Reew of Equton Etblh the coordnte ytem ruler Drw elocty rrow. Accelerton drecton cn be clculted from elocty becue Δ Mke up mple number: 1-5 m/ -8 m/ V-1 [ -8 (-5)] m/ Δ -3 m/ o negte Accel. I negte Fundmentl Defnton of Aerge Velocty. Th not Δ! Fundmentl Defnton of Aerge Accelerton. Δ Equton Notton Reew of Equton Smplfy by ettng t 1 0 Thnk of t t Other mplfed notton nd umpton f g nd Contnt Δ Δ t Δ + 0 f 0 A combnton of other equton My be ued only Accelerton contnt Intl t zero or t men only f: t 1 + t Equton: from your text A combnton or rerrnged My be ued only f: Accelerton contnt Intl t zero or t men Rte of Chnge of Rte of Chnge of Velocty Slope Re/Run Δ 5

6 Red from Grph Coordnte On n x t grph the coordnte tell u the poton (x) nd the tme ntnt (t). Slope On n x t grph the lope tell u the elocty. Are UNITS Ge u the CLUES! Red from Grph Coordnte On n t grph the coordnte tell u the nd the Slope On t grph the lope tell u the. Are UNITS Ge u the CLUES! Red from Grph Coordnte On n t grph the coordnte tell u the elocty nd the tme ntnt Slope On t grph the lope tell u the ccelerton. Are UNITS Ge u the CLUES! Sgn? Depend on Coordnte Sytem Choce Wht the gn of: x, xf,,, f, Δ,? Sgn? Depend on Coordnte Sytem Choce Sgn? Depend on Coordnte Sytem Choce Wht the gn of: x, xf,,, f, Δ,? Wht the gn of: x, xf,,, f, Δ,? 0, +, +, +, +, -, - 6

7 Sgn? Depend on Coordnte Sytem Choce Sgn? Depend on Coordnte Sytem Choce Wht the gn of: x, xf,,, f, Δ,? -, +, +, +, +, -, - Wht the gn of: x, xf,,, f, Δ,? Sgn? Depend on Coordnte Sytem Choce Now cn you plot th? Depend on Coordnte Sytem Choce Wht the gn of: x, xf,,, f, Δ,? +, -, -, -, -, +, + x. t. t?? Now cn you plot th? Depend on Coordnte Sytem Choce Exmple: 1 prt problem Problem Decrpton A peron trelng left begnnng t 10 m/ nd lowng down for mn. before toppng. How fr doe th peron trel? x. t. t 7

8 Phyc Decrpton Slowng 0 0 m/ 10 m/ 10 ec 0 Δ t 1 + t Note: Velocte re pote. Accelerton neg. nce Δ neg. Slowng 0 0 m/ 10 m/ 10 ec 0 Soluton Δ t 1 + t Ue crcled equton Fnd erge elocty frt m m m 5 Now cn fnd dplcement m 5 (10 0) 600m Elute A peron trelng left begnnng t 10 m/ nd lowng down for mn. before toppng. How fr doe th peron trel? Unt Anly m m Mgntude 600 m le thn when peed w contnt. Exmple : Mult-Prt Prob Problem Decrpton A truck on trght rod trt from ret nd ccelerte t.0 m/ untl t reche peed of 0 m/. Then the truck trel for 0 t contnt peed untl the brke re ppled, toppng the truck n unform mnner n n ddtonl 5.0. Wht the erge elocty of the truck durng the moton decrbed? Phyc Decrpton Phyc Decrpton Prt 1: Moton Type? Coordnte Sytem? Strobe Photo? Velocty ector? Accel. Vector? Speed Up 0 0 m/ 0 m/ 0 ec m/ Prt 1: Moton Type? Coordnte Sytem? Strobe Photo? Velocty ector? Accel. Vector? Δ Δ t 1 + t t 1 + t 8

9 Phyc Decrpton: Prt Phyc Decrpton: Prt Speed Up Speed Up Contnt 0 x 0 m/ 0 m/ 0 ec t m/ 0 x 0 m/ 0 m/ 0 m/ 0 ec t (nother m/ 0 0) Δ Δ Δ Δ t 1 + t t 1 + t t 1 + t t 1 + t Phyc Decrpton: Prt 3 Speed Up Contnt Slow Down 0 x 0 m/ 0 m/ 0 m/ 0 0 ec t (nother (nother 5) m/ 0 0) Soluton Crcle thng known n equton Sole for wht you cn Keep gong untl eerythng known Δ Δ Δ t 1 + t t 1 + t t 1 + t Soluton Elute Speed Up Contnt Slow Down 0 0 m/ 0 ec m/ 100 m 0 m/ t m 0 m/ 30-4 m/ 550 m 0 35 Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? Δ Δ Δ t 1 + t t 1 + t t 1 + t 9

10 Exmple 3: Free Fll Problem Decrpton Moton Type I Contnt or Speed up or Slow y Prt I: Equton Crcle the known lue Δ t 1 + t An pple fll from tree from dtnce of.0 m boe the top of the gr below. Whle fllng, t h downwrd ccelerton of 9.8 m/. A the pple nk nto the gr, t peed decree untl t top fter nkng m nto the gr. Sole for eerythng. Moton Type II Contnt or Speed up or Slow Moton Type III Contnt or Speed up or Slow y y Prt II: Equton Crcle the known lue Δ 1 t + t Prt III: Equton Crcle the known lue Δ 1 t + t Soluton Crcle thng known n equton Sole for wht you cn Moton Type I Speed up 9.8 m/ y m/ 0.64 Moton Type II Keep gong untl eerythng known +391 m/ Slow y.0 m 0 0 Prt I: Equton Crcle the known lue Δ 1 t + t Prt II: Equton Crcle the known lue Δ t 1 + t y m Wth Dfferent y0 Elute Moton Type I Speed up Moton Type II Slow y.05 m m/ y 0.05 m -6.6 m/ m/ Prt I: Equton Crcle the known lue Δ t 1 + t Prt II: Equton Crcle the known lue Δ t 1 + t Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? y 0 m