a PHYS 1: Lecure 2 Moion a Consan Acceleraion a Area = a a v = ad v v = a v x = vd A=(1/2)( v) Area = v v = v-v v x x = v + a 1 2 2 Relaive Moion: Reference Frames x d Achilles Toroise x Toroise Reference frame = Earh Reference frame = Achilles
Music Who is he Aris? A) Sephane Grappelli B) Pearl Django C) Mark O ConnorO Connor s s Ho Swing Trio D) Miles Davis E) Cassandra Wilson Absoluely Incredible Album!! Mark O Connor O Wynon Marsalis Jane Monhei fiddle rumpe vocals
1-D Moion Example: Consan Acceleraion An Example of Applicaion of Kinemaic Definiions ha ARE ALWAYS TRUE!!! Acceleraion: r a r dv d SPECIAL CASE Assume consan acceleraion a = a a a Area = a a v Velociy: r v r dx d SPECIAL CASE v = v-v A=(1/2)( v) Area = v v v = ad v v = a x = vd x x = v + a 1 2 2 v = v + a v 2 = v 2 + 2a( x x) x = x + 1 2 + v 2 a
Preflighs 1 & 3 A dragser sars from res and moves wih consan acceleraion and crosses he finish line (1/4 mile) in 3 seconds.. 1. I will reach half of is maximum speed a he 1/8 mile mark. 3. I will reach half of is maximum speed in 1.5 seconds. (A) Boh True (B) Boh False (C) 1 True 3 False QUESTION: Wha are possible problems wih hese explanaions? Because he car is acceleraing consanly, his means ha he velociy of he car is increasing coninuously a he same rae, because of his a he halfway poin in he race, he car would reach half is minimum speed. (D) 1 False 3 True 5 4 3 2 1 If he acceleraion is consan, is velociy will be coninually increasing hroughou he race, meaning i will be going relaively "faser" owards he end of he race. This higher velociy means a greaer coverage of disance per uni of ime, so he racers half speed will occur somewhere before he halfway poin in he race. ANSWER: Halfway Poin : halfway in ime is no same as halfway in disance!! A B C D YOU CAN CHECK THIS WITH MOVING MAN!! Download from hp://phe.colorado.edu/en/simulaion/moving-man
Preflighs 1 & 3: Takeaway Message? BE CAREFUL! Posiion, Velociy, Acceleraion, Time are differen quaniies. e.g., halfway poin NOT well-defined Halfway in Time Posiion is NOT linear in ime Halfway in Posiion Half posiion DOES NOT occur a half ime Velociy is linear in ime Halfway in Speed Half speed occurs a half ime
Follow Up A dragser sars from res and moves wih consan acceleraion and crosses he finish line (1/4 mile) in 3 seconds.. 1. I will reach he 1/8 mile mark when i reaches half of is maximum speed. 3. I will reach he 1/8 mile mark in 1.5 seconds. (A) Boh True (B) Boh False 1 True (C) 3 False Time for Half Speed (D) 1 False 3 True Time for Half Posiion Halfway in Posiion Halfway in Speed
Relaive Moion: Reference Frames There is only one equaion: v TA = v T v A Check his ou a he Achilles/Toroise link in he Lecure column of he Course Planner
Prefligh 5 x = QUESTIONS ABOUT = in reference frame of B (A) x A < (B) x A = (C) x A > x A = -d (A) v A < (B) v A = (C) v A > v A = +5 m/s
Prefligh 5 x A = -d v A = +5 m/s QUESTIONS ABOUT = in reference frame of B (A) x C < (B) x C = (C) x C > x C = +d (A) v C < (B) v C = (C) v C > v C = -4 m/s
Prefligh 5 A =: x A = -d v A = +5 m/s x C = +d v C = -4 m/s Which ball (A or C) will hi B firs? (A) (B) (C) A his B before C his B C his B before A his B C his B a he same ime as A his B Le s draw his from he 5 m/s 4 m/s reference frame of B! A B C d d
Prefligh 5 Which of he graphs o he righ represen he moion of balls A and C as observed in he reference frame of ball B? A =: Suden reasons: x A = -d v A = +5 m/s x C = +d v C = -4 m/s (e) None of he above The answer is C because in boh a and b he slope or velociy of ball A is negaive and i is moving in a posiive direcion and he slope or velociy of C is posiive bu moving in a negaive direcion. I is no D because C as a seeper slope of 6m/s as opposed o A who has only 5m/s A is approaching B a a faser rae (seeper slope) han ball C. This narrows i down o graphs (a) and (d). (d) is hen he answer, because A is approaching from a negaive disposiion. 35 3 25 2 15 1 5 A B C D E
Prefligh 5 Which of he graphs o he righ represen he moion of balls A and C as observed in he reference frame of ball B? A =: x A = -d v A = +5 m/s x C = +d v C = -4 m/s (e) None of he above WHAT DOES MOTION LOOK LIKE IN REFERENCE FRAME OF B? v A > and v C < A 5 m/s 4 m/s B C velociy = slope of x vs plo Speed(A) > Speed(C) d d speed = magniude of slope of x vs plo