a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114
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1 Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module 3-Phy4-Eyre Rte o Chnge o Rte o Chnge o Velocty Slope Re/Run (m/) 4/3/07 Module 3-Phy4-Eyre 3 t() Accelerton Etblh the coordnte ytem ruler Drw elocty rrow. Accelerton drecton cn be clculted rom elocty becue 0 Mke up mple number: - 5 m/ -8 m/ - [ -8 (-5)] m/ -3 m/ o negte Accel. I negte 4/3/07 Module 3-Phy4-Eyre 4 Chngng Velocty Fndng the Aerge, 4, 7, 8, 9, 5, 35, 4, 7, 0, 3, 6, 9 4, 8,, 6, 0, 4, 8 Requlrly chngng elocty: Aerge the t + nd Lt The mddle lue Velocty regulrly ncree rom 0 to 0 m/: g? All thee Velocte? Chnge n Velocty: lter elocty mnu erler elocty Aerge Velocty: Between ny tme Slope o trght lne between pont I elocty ncree regulrly then you my lo nd erge o nd. Intntneou Velocty Between tme jut bt ter/beore t Slope o tngent lne t t lter erler ( + ) 4/3/07 Module 3-Phy4-Eyre 5 4/3/07 Module 3-Phy4-Eyre 6
2 Sgn? Depend on Coordnte Sytem Choce Sgn? Depend on Coordnte Sytem Choce 0 Wht the gn o:,,,,,,? 0, +, +, +, +, -, - 4/3/07 Module 3-Phy4-Eyre 7 0 Wht the gn o:,,,,,,? -, +, +, +, +, -, - 4/3/07 Module 3-Phy4-Eyre 8 Sgn? Plot ll three grph Depend on Coordnte Sytem Choce 0 0 Wht the gn o:,,,,,,? +, -, -, -, -, +, + 4/3/07 Module 3-Phy4-Eyre 9. t. t. t 4/3/07 Module 3-Phy4-Eyre 0 Wht Red rom Grph? t grph t grph t grph Red rom Grph UNITS Ge u the CLUES! Coordnte Slope Red poton t tme ntnt X(m) Slope m Slope m Are t () t () t () Are Are UNITS Ge u the CLUES! 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module 3-Phy4-Eyre
3 Vrton n Equton Notton Notton nd umpton I ccelerton contnt, then g The equton cn be rerrnged to look derent Etr ubcrpt re ometme dded to pecy horzontl or ertcl moton /3/07 Module 3-Phy4-Eyre 3 Combnng to get new equton A combnton yeld hndy new equton Strt wth undmentl equton Aume contnt ccel. Elmnte delt t n the equton Rerrnge lot! ( ) ( ) /3/07 Module 3-Phy4-Eyre 4 Combnng to get new equton A combnton yeld hndy new equton Strt wth undmentl equton Aume contnt ccel. Elmnte nl n the equton Rerrnge lot! + + ( ) + ( ) /3/07 Module 3-Phy4-Eyre 5 Ue re to nd equton or dplcement Aume contnt ccelerton o trght t grph lne /3/07 Module 3-Phy4-Eyre 6 t Equton: rom your tet Equton: reduced et A combnton or rerrnged My be ued only : Accelerton contnt ( ) ( ) ( ) + ( ) ( ) ( ) Fundmentl denton + + 4/3/07 Module 3-Phy4-Eyre 7 4/3/07 Module 3-Phy4-Eyre 8 3
4 Problem Solng Proce Prepre Sketch Drw Dgrm Sole Wrte Equton Crcle wht known Algebr Elute-Ae Unt Mgntude Sgn Emple: prt problem Problem Decrpton A peron trelng let begnnng t 0 m/ nd lowng down or mn. beore toppng. How r doe th peron trel? 4/3/07 Module 3-Phy4-Eyre 9 4/3/07 Module 3-Phy4-Eyre 0 0 m/ t 0 ec Slowng Dgrm 0-0 m/ t 0 t + t Note: Velocte re neg. Accelerton + nce + 4/3/07 Module 3-Phy4-Eyre Slowng 0 0 m/ -0 m/ t 0 ec t 0 + t Soluton Ue crcled equton Fnd erge elocty rt m m m 5 Now nd dplcement m 5 (0 0) 600m 4/3/07 Module 3-Phy4-Eyre Elute A peron trelng let begnnng t 0 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 (00m3/4 m). Sgn negte whch mtche dgrm. 4/3/07 Module 3-Phy4-Eyre 3 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? 4/3/07 Module 3-Phy4-Eyre 4 4
5 Phyc Decrpton: 3 Prt Soluton Speed Up Contnt Slow Down Speed Up Contnt Slow Down 0 0 m/ t 0 ec m/ 0 m/ t t 0 0 m/ t (nother 0) 0 t (nother 5) 0 0 m/ t 0 ec m/ 00 m 0 m/ t t m 0 m/ t 30-4 m/ 550 m 0 t 35 + t + t + t + t + t + t 4/3/07 Module 3-Phy4-Eyre 5 4/3/07 Module 3-Phy4-Eyre 6 Elute Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? 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. 4/3/07 Module 3-Phy4-Eyre 7 4/3/07 Module 3-Phy4-Eyre 8 Problem olng proce Coordnte + down, y0 md Prepre Sketch Drw Dgrm Sole Wrte Equton Crcle wht known Algebr Elute-Ae Unt Mgntude Sgn 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 + Prt II: Equton Crcle the known lue + 4/3/07 Module 3-Phy4-Eyre 9 4/3/07 Module 3-Phy4-Eyre 30 5
6 Coordnte + down, y0 bottom Coordnte + up, y0 bottom Type I Speed up y -.05 m 0 t m/ Prt I: Equton Crcle the known lue + Type I Speed up y +.05 m 0 t m/ Prt I: Equton Crcle the known lue + Type II Slow y m +6.6 m/ t m/ Prt II: Equton Crcle the known lue + Type II Slow y m -6.6 m/ t m/ Prt II: Equton Crcle the known lue + y 0 m 0 t 0.66 y 0 m 0 t /3/07 Module 3-Phy4-Eyre 3 4/3/07 Module 3-Phy4-Eyre 3 Elute Unt Anly? Mgntude Reonble? Do the Sgn mtch the Arrow? 4/3/07 Module 3-Phy4-Eyre 33 6
Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!
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
x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions
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,
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