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


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1 Lecure 3: 1D 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, P9d, 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 Spceime digrms spce () ime  Grph shows he eoluion of he posiion (1D) 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 spceime digrms spce ()  Keep o 1D for he momen: 1 mil 20 m 30 m 50 m ime  Spceime digrm for rip o Lile Cesr s (wlking consn re, nd wiing in line)
6 Clicker Quesion: 3) Which of he following spceime digrms represen n objec which ulimely comes o sop nd remins sopped? ) b) c) d) e)
7 Clicker Quesion: 3) Which of he following spceime 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 = 21
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 = nideriie 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 1D: 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 1D: 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 spceime digrm) d d Accelerion (slope on elociyime digrm) d d
15 Clicker Quesion: 5) The following is elociy s. ime digrm for n objec moing in 1D: 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 1D: 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 1D: 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 2D: 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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