Chapter 2. Kinematics in One Dimension
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1 Chaper. Kinemaics in One Dimension In his chaper we sudy kinemaics of moion in one dimension moion along a sraigh line. Runners, drag racers, and skiers are jus a few eamples of moion in one dimension. Chaper Goal: To learn how o sole problems abou moion in a sraigh line. Chaper. Kinemaics in One Dimension Topics: Uniform Moion Insananeous Velociy Finding Posiion from Velociy Moion wih Consan Acceleraion Free Fall Moion on an Inclined Plane Insananeous Acceleraion Moion along a sraigh line Posiion graph Origin (= cm s s 3 s 4 s cm 4 cm 7 cm Can be illusraed by posiionersus-ime graph: Coninuous (smooh cure 3 4 (s 3 = 3 4 (s Sraigh line uniform moion he same elociy Velociy is he slope sec sec 3 sec Velociy is he same zero acceleraion r r aag r 4 sec 4
2 Posiion graph: uniform moion Uniform moion: moion wih consan elociy > < Moions in opposie direcions = + ( (s 5 6 Posiion graph unrealisic realisic 7 8
3 Insananeous elociy Finding posiion from elociy Very small Insananeous elociy: = = d( = ( ( d d If dependence ( is gien, hen d( - deriaie d Insananeous elociy - slope Eample: 4 ( = 5 ( = 5sin( d( 3 d d( 5cos( d 9 Eample: C D ( ( = = ( d Find he ne displacemen A B The displacemen is he area, displacemen is posiie = = ( d > ( ( Displacemen is negaie = = ( d < ( > ( < B B A B = B A = ( d = = m A C area B C = C B = ( d = = m B D C D = D C = ( d = ( 4 = m C = = + + = + + A D D A D C C B B A C D B C A B = + + = m
4 A B C Velociy is he slope ds = d Velociy is he slope ds = d < < A B C < > A C Acceleraion is he slope d a d 3 4 Moion wih consan acceleraion Moion wih consan elociy or consan acceleraion Moion wih consan elociy: Moion wih consan acceleraion: a d = d = + ( = + a ( ( ( ( ( = + d = + + a d = + + a =? Moion wih consan elociy: = + ( Moion wih consan acceleraion: = + a( = + ( + a( Useful relaion: ( = a ( = + + a a hen = a( 5 6
5 Moion wih consan elociy or consan acceleraion Moion wih consan elociy: = + Moion wih consan = + a acceleraion: = + + a = a( = Free fall moion - moion wih consan acceleraion r g = consan y a = g = 9.8 m s = g = g( y y y = y + g 7 8 Free fall moion - moion wih consan acceleraion final = = m / s y = g = 9.8 m s = g = g( y y y = y + g EXAMPLE.4 Friday nigh fooball QUESTION: A final poin: final = = 9.8 f = y 9.8 f y = 4.9 f f f y = 4.9 = 9.8 = 9.8 y 9
6 EXAMPLE.4 Friday nigh fooball EXAMPLE.4 Friday nigh fooball EXAMPLE.4 Friday nigh fooball EXAMPLE.4 Friday nigh fooball
7 EXAMPLE.4 Friday nigh fooball EXAMPLE.4 Friday nigh fooball Moion on an Inclined Plane EXAMPLE.7 Skiing down an incline QUESTION:
8 EXAMPLE.7 Skiing down an incline EXAMPLE.7 Skiing down an incline EXAMPLE.7 Skiing down an incline EXAMPLE.7 Skiing down an incline
9 General Principles Chaper. Summary Slides General Principles Imporan Conceps
10 Imporan Conceps Applicaions Applicaions Chaper. Quesions
11 Which posiion-ersus-ime graph represens he moion shown in he moion diagram? Which posiion-ersus-ime graph represens he moion shown in he moion diagram? Which elociy-ersus-ime graph goes wih he posiion-ersus-ime graph on he lef? Which elociy-ersus-ime graph goes wih he posiion-ersus-ime graph on he lef?
12 Which posiion-ersus-ime graph goes wih he elociy-ersus-ime graph a he op? The paricle s posiion a i = s is i = m. Which posiion-ersus-ime graph goes wih he elociy-ersus-ime graph a he op? The paricle s posiion a i = s is i = m. Which elociy-ersus-ime graph or graphs goes wih his acceleraion-ersusime graph? The paricle is iniially moing o he righ and eenually o he lef. Which elociy-ersus-ime graph or graphs goes wih his acceleraion-ersusime graph? The paricle is iniially moing o he righ and eenually o he lef.
13 The ball rolls up he ramp, hen back down. Which is he correc acceleraion graph? The ball rolls up he ramp, hen back down. Which is he correc acceleraion graph? Rank in order, from larges o smalles, he acceleraions a A a C a poins A C. Rank in order, from larges o smalles, he acceleraions a A a C a poins A C. A a A > a B > a C B a A > a C > a B C a B > a A > a C D a C > a A > a B E a C > a B > a A A a A > a B > a C B a A > a C > a B C a B > a A > a C D a C > a A > a B E a C > a B > a A
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Chapter 2 Kinematics in One Dimension
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