Lecture 3: 1-D Kinematics. This Week s Announcements: Class Webpage: visit regularly

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1 Lecure 3: 1-D Kinemics This Week s Announcemens: Clss Webpge: hp://kesrel.nm.edu/~dmeier/phys121/phys121.hml isi regulrly Our TA is Lorrine Bowmn Week 2 Reding: Chper 2 - Gincoli Week 2 Assignmens: Due: 9/1 - HW #1 (chp 1: Q5, P2, P8, P39 & chp 2: Q2, Q18, P7, P9-d, P35, P42) - for his one ssignmen you mus repor your nswers wih proper unis nd sig. figs. for full credi!! - MseringPhysics: -Inroducion o Msering Physics (if no done ye)

2 This Week s Gol: - Define nd inroduce he bsic kinemic ribles, such s displcemen, elociy nd ccelerion, nd begin pplying hem o one dimensionl moion. Wee! I m lerning kinemics

3 Spce-ime digrms spce () ime - Grph shows he eoluion of he posiion (1-D) in ime (how hings moe in ime) --- no ( s. y) bu s. ime

4 - Posiion: The spil coordine of n objec s funcion of ime []. -generlly he he freedom o selec he zero of our coordine sysem s we like Disnce nd Displcemen + - Disnce: The lengh coered long ph. -lwys posiie quniy X o = +1 mil from = -1 mil - Displcemen: The ne chnge in posiion (nd direcion) for ph [Δ = - o ]. -Displcemen of round rip is zero! X =0 -

5 Inroducion o spce-ime digrms spce () - Keep o 1-D for he momen: 1 mil 20 m 30 m 50 m ime - Spce-ime digrm for rip o Lile Cesr s -(wlking consn re, nd wiing in line)

6 Clicker Quesion: 3) Which of he following spce-ime digrms represen n objec which ulimely comes o sop nd remins sopped? ) b) c) d) e)

7 Clicker Quesion: 3) Which of he following spce-ime digrms represen n objec which ulimely comes o sop nd remins sopped? ) b) c) d) e)

8 Velociy nd Speed - Aerge speed, s: (disnce reled)/(ol ime) Slope = rise/run = Δ/Δ 2 -lwys posiie quniy Δ = Aerge elociy: (displcemen)/(ol ime) -includes direcion informion 1 2 Δ = 2-1

9 - insnneous elociy,, (or simply elociy ): (The chnge in displcemen oer ery iny ime inerl) /(h iny ime inerl) -includes direcion informion d d (+h) - () = Δ - insnneous speed,, (or simply speed ): The mgniude of he insnneous elociy. -lwys posiie quniy V = lim h 0 h = Δ Slope = rise/run = Δ/Δ (+h) - () h -This is precisely he definiion of he ime deriie of. V = d/d

10 Clculus Digression () = d()/d =1 Slope = 2/2 = 1 * 2 Slope = 2/2 = 1 * 2 2 * 2 2 Slope = 2/2 = 1 2 Slope = rise/run Slope oer infiniesiml disnce=d()/d V = lim h 0 (+h) - () d h = d () = 2 d()/d =2 - When he cure is horizonl, Δ is zero, so he slope Δ/Δ = 0 Slope = 4/1 = 4 * 4 -seing he deriie o zero finds he locl minim or mim = inegrl = ni-deriie Slope = -2/1 = * * 1 * Slope = 0/1 = Slope = 2/1 = 2

11 Clicker Quesion: 4) The following is spce ime digrm for n objec moing in 1-D: Which of he following represens he elociy s. ime digrm for he objec? ) b) c) d) e)

12 Clicker Quesion: 4) The following is spce ime digrm for n objec moing in 1-D: Which of he following represens he elociy s. ime digrm for he objec? ) b) c) d) e)

13 Accelerion - Accelerion is he chnge in elociy wih ime, in compleely nlogous fshion o elociy being chnge in displcemen wih ime - erge ccelerion: (chnge in elociy)/(ol ime) -includes direcion informion d d (+h) - () - insnneous ccelerion,, (or simply ccelerion ): (The chnge in elociy oer ery iny ime inerl) /(h iny ime inerl) -includes direcion informion = lim h 0 h (+h) - () h d = d -This is precisely he definiion of he ime deriie of. d = 2 d 2 =

14 Velociy (slope on spce-ime digrm) d d Accelerion (slope on elociy-ime digrm) d d

15 Clicker Quesion: 5) The following is elociy s. ime digrm for n objec moing in 1-D: Which of he following represens he ccelerion s. ime digrm for he objec? ) b) c) d) e)

16 Clicker Quesion: 5) The following is elociy s. ime digrm for n objec moing in 1-D: Which of he following represens he ccelerion s. ime digrm for he objec? ) b) c) d) e)

17 Emple: Non consn ccelerion

18 6) Which of he following represens he ime re of chnge of he ccelerion (d 3 /d 3 ) [k he jerk ]? ) c) e) Clicker Quesion: - (d 3 /d 3 ) + b) - (d 3 /d 3 ) + d) - (d 3 /d 3 ) + - (d 3 /d 3 ) + - (d 3 /d 3 ) +

19 ) c) e) Clicker Quesion: 6) Which of he following represens he ime re of chnge of he ccelerion (d 3 /d 3 ) [k he jerk ]? - (d 3 /d 3 ) + b) - (d 3 /d 3 ) + d) - (d 3 /d 3 ) + - (d 3 /d 3 ) + - (d 3 /d 3 ) +

20 1-D: elociy Moion digrms - speeding up: ccelerion presen - ccelerion sign (+) if elociy increses in direcion of incresing coordine elociy - slowing down: ccelerion presen - ccelerion sign (-) if elociy decreses in direcion of incresing coordine - A grph he represens he locion of n objec series of equl spced seps in ime 2-D: y elociy

21 Generl Definiions: () = he posiion of n objec s funcion of ime () = d () = d d d d = = d d d d 2 ( ) d 2 -Or- = d = d = [ d] d

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