Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
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1 Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed Vector: Mgntude nd Drecton Poton, Dplcement,, Accelerton Don t Forget Unt! Coordnte Sytem Etblh the coordnte ytem ruler A number lne wth n ndcton howng pote drecton. Any drecton you chooe. The 0 (or y0) locton dented. Agn t cn be ny plce your chooe. 0 Poton Etblh the coordnte ytem ruler Red the poton rom the ruler Don t orget the unt nd drecton Negte Poton Pote Poton Etblh the coordnte ytem ruler drecton pote n drecton o coordnte ytem. drecton cn lo be clculted rom dplcement becue Pote Negte 1
2 Denton o g. elocty Both de o equton re equl Mgntude Unt Drecton (t ector!) Mgntude Mgntude Unt Unt Drecton Drecton Rte o Chnge o Rte o Chnge o Poton Slope Re/Run (m) t() Chngng All thee Velocte? 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 ncree rom 10 to 0 m/: g.? + Chnge n : lter elocty mnu erler elocty Aerge : Between ny tme I elocty ncree regulrly then nd erge o nd. Slope o trght lne between pont Intntneou Between tme jut bt ter/beore t Slope o tngent lne t t Δ lter erler ( + ) Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Δ Mgntude Mgntude Unt Unt Drecton Drecton Rte o Chnge o Rte o Chnge o Slope Re/Run (m/) Δ t()
3 Accelerton Etblh the coordnte ytem ruler Drw elocty rrow. Accelerton drecton cn be clculted rom elocty becue Δ 0 Mke up mple number: 1-5 m/ -8 m/ V-1 [ -8 (-5)] m/ Δ -3 m/ o negte Accel. I negte Sgn? Depend on Coordnte Sytem Choce 0 Wht the gn o:,,,,, Δ,? 0, +, +, +, +, -, - Sgn? Depend on Coordnte Sytem Choce Sgn? Depend on Coordnte Sytem Choce 0 Wht the gn o:,,,,, Δ,? -, +, +, +, +, -, - 0 Wht the gn o:,,,,, Δ,? +, -, -, -, -, +, + Red rom Grph Red rom Grph UNITS Ge u the CLUES! Coordnte On n t grph the coordnte tell u the poton () nd the tme ntnt (t). Slope On n t grph the lope tell u the elocty. Are UNITS Ge u the CLUES! X(m) Slope m Slope m t () t () t () Are Are 3
4 Plot ll three grph Equton Notton 0. t. t. t Common n other tet Smply by ettng t 10 Thnk o t t Other mpled notton nd umpton g nd Contnt Δ Δ t t Δ t t + t 0 0 Equton: rom your tet A combnton or rerrnged My be ued only : Accelerton contnt ( ) ( ) + Δ t Fundmentl denton 1 1 Δ + t + t + Δ ( ) + ( ) ( ) ( ) Δ Problem Solng Proce Problem Decrpton: Th generlly gen. You mut denty n the tet 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.. Elute A peron trelng let t 10 m/ or mn. How r doe th peron trel? Unt Anly m m Mgntude 100 m bout 3/4 m Mut be rdng n ehcle Emple: 1 prt problem Problem Decrpton A peron trelng let begnnng t 10 m/ nd lowng down or mn. beore toppng. How r doe th peron trel? 4
5 Dgrm nd Pctorl Dgrm Speclzed Dgrm tht nclude mot o the knemtc normton. Ued tool to ole knemtc t problem. /Pctorl Dgrm templte re lble to prnt rom the cl webte. Dgrm Type I Contnt or Speed up or Slow Type II Contnt or Speed up or Slow Type III Contnt or Speed up or Slow t t Prt I: Equton Crcle the known lue Prt II: Equton Crcle the known lue Prt III: Equton Crcle the known lue t Phyc Decrpton Slowng 0 0 m/ -10 m/ t 10 ec t 0 Δ t 1 + t Note: Velocte re neg. Accelerton + nce Δ + Slowng 0 0 m/ -10 m/ t 10 ec t 0 Δ 1 t Soluton Ue crcled equton Fnd erge elocty rt m m m 5 Now nd dplcement m 5 (10 0) 600m Elute A peron trelng let begnnng t 10 m/ nd lowng down or mn. beore toppng. How r doe th peron trel? Unt Anly m m Mgntude 600 m le thn wht t would be t contnt peed (100m3/4 m). Sgn negte whch mtche dgrm. Emple : Mult-Prt Prob Problem Decrpton A truck on trght rod trt rom ret nd ccelerte t.0 m/ untl t reche peed o 0 m/. Then the truck trel or 0 t contnt peed untl the brke re ppled, toppng the truck n unorm mnner n n ddtonl 5.0. Wht the erge elocty o the truck durng the moton decrbed? Phyc Decrpton: 3 Prt Speed Up Contnt Slow Down 0 0 m/ 0 m/ 0 m/ 0 t 0 ec t t t (nother t (nother 5) m/ 0 0) Δ Δ Δ 1 t 1 t 1 t 5
6 Soluton Elute Speed Up Contnt Slow Down 0 0 m/ t 0 ec m/ 100 m 0 m/ t t m 0 m/ t 30-4 m/ 550 m 0 t 35 Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? Δ Δ Δ 1 t 1 t 1 t Emple 3: Free Fll Problem Decrpton An pple ll rom tree rom dtnce o.0 m boe the top o the gr below. Whle llng, t h downwrd ccelerton o 9.8 m/. A the pple nk nto the gr, t peed decree untl t top ter nkng m nto the gr. Sole or eerythng. Soluton Crcle thng known n equton Sole or wht you cn Keep gong untl eerythng known Coordnte + down, y0 md Type I Speed up Type II Slow y -.0 m 0 t m/ y m/ t m/ y m 0 t 0.66 Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + Coordnte + down, y0 bottom Type I Speed up Type II Slow y -.05 m 0 t m/ y m +6.6 m/ t m/ y 0 m 0 t 0.66 Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + 6
7 Coordnte + up, y0 bottom Elute Type I Speed up Type II Slow y +.05 m 0 t m/ y m -6.6 m/ t m/ Prt I: Equton Crcle the known lue Δ 1 + Prt II: Equton Crcle the known lue Δ 1 + Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? y 0 m 0 t
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