Chapter 2 One-Dimensional Kinematics Description of motion in one dimension

Transcription

1 Chaper 2 One-Dimensional Kinemaics Descripion of moion in one dimension

2 Unis of Chaper 2 Posiion, Disance, and Displacemen Average Speed and Velociy Insananeous Velociy Acceleraion Moion wih Consan Acceleraion Applicaions of he Equaions of Moion Freely Falling Objecs

3 2-1 Posiion, Disance, and Displacemen Before describing moion, you mus se up a coordinae sysem define an origin and a posiive direcion. Posiion: described by x

4 2-1 Posiion, Disance, and Displacemen The disance is he oal lengh of ravel; if you drive from your house o he grocery sore and back, you have covered a disance of 8.6 mi.

5 2-1 Posiion, Disance, and Displacemen Displacemen is he change in posiion. If you drive from your house o he grocery sore and hen o your friend s house, your displacemen is 2.1 mi and he disance you have raveled is 10.7 mi. displacemen = change in posiion = final posiion iniial posiion displacemen = Δx = Δxf xi

6 Quesion 2.1 Walking he Dog You and your dog go for a walk o he park. On he way, your dog akes many side rips o chase squirrels or examine fire hydrans. When you arrive a he park, do you and your dog have he same displacemen? a) yes b) no

7 Quesion 2.1 Walking he Dog You and your dog go for a walk o he park. On he way, your dog akes many side rips o chase squirrels or examine fire hydrans. When you arrive a he park, do you and your dog have he same displacemen? a) yes b) no Yes, you have he same displacemen. Because you and your dog had he same iniial posiion and he same final posiion, hen you have (by definiion) he same displacemen. Follow-up: have you and your dog raveled he same disance?

8 2-2 Average Speed and Velociy The average speed is defined as he disance raveled divided by he ime he rip ook: Average speed = disance / elapsed ime Is he average speed of he red car 40.0 mi/h, more han 40.0 mi/h, or less han 40.0 mi/h?

9 2-2 Average Speed and Velociy The average speed is defined as he disance raveled divided by he ime he rip ook: Average speed = disance / elapsed ime Is he average speed of he red car 40.0 mi/h, more han 40.0 mi/h, or less han 40.0 mi/h? 4.00mi 1 = = (4.00 / 30.0) h 30.0mi / h 4.00mi 2 = = (4.00 / 50.0) h 50.0mi / h 8mi = h Average speed = = 37.6mi / h < 40mi / h 0.213h

10 2-2 Average Speed and Velociy Average velociy = displacemen / elapsed ime If you reurn o your saring poin, your average velociy is zero. average velociy v av Δx = = Δ x f f displacemen = elapsed ime x i i

11 2-2 Average Speed and Velociy Graphical Inerpreaion of Average Velociy The same moion, ploed one-dimensionally and as an x- graph:

12 2-3 Insananeous Velociy Definiion: (2-4) This means ha we evaluae he average velociy over a shorer and shorer period of ime; as ha ime becomes infiniesimally small, we have he insananeous velociy.

13 2-3 Insananeous Velociy This plo shows he average velociy being measured over shorer and shorer inervals. The insananeous velociy is angen o he curve. v = lim Δ 0 Δx Δ displacemen average velociy = elapsed ime v av Δx = = Δ x f f x i i

14 2-3 Insananeous Velociy Graphical Inerpreaion of Average and Insananeous Velociy

15 Average acceleraion: 2-4 Acceleraion (2-5)

16 2-4 Acceleraion Graphical Inerpreaion of Average and Insananeous Acceleraion: a = lim Δ 0 Δv Δ a av Δv = = Δ v f f v i i

17 2-4 Acceleraion Acceleraion (increasing speed) and deceleraion (decreasing speed) should no be confused wih he direcions of velociy and acceleraion:

18 Unis of Chaper 2 Posiion, Disance, and Displacemen Average Speed and Velociy Insananeous Velociy Acceleraion Moion wih Consan Acceleraion Applicaions of he Equaions of Moion Freely Falling Objecs

19 Review: 2-3 Insananeous Velociy This plo shows he average velociy being measured over shorer and shorer inervals. The insananeous velociy is angen o he curve. v = lim Δ 0 Δx Δ displacemen average velociy = elapsed ime v av Δx = = Δ x f f x i i

20 Review: 2-4 Acceleraion Graphical Inerpreaion of Average and Insananeous Acceleraion: a = lim Δ 0 Δv Δ a av Δv = = Δ v f f v i i

21 Quesion 2.13a Graphing Velociy I The graph of posiion versus ime for a car is given below. Wha can you say abou he velociy of he car over ime? a) i speeds up all he ime b) i slows down all he ime c) i moves a consan velociy d) someimes i speeds up and someimes i slows down e) no really sure x

22 Quesion 2.13a Graphing Velociy I The graph of posiion versus ime for a car is given below. Wha can you say abou he velociy of he car over ime? a) i speeds up all he ime b) i slows down all he ime c) i moves a consan velociy d) someimes i speeds up and someimes i slows down e) no really sure x The car moves a a consan velociy because he x vs. plo shows a sraigh line. The slope of a sraigh line is consan. Remember ha he slope of x vs. is he velociy!

23 Quesion 2.13b Graphing Velociy II The graph of posiion vs. ime for a car is given below. Wha can you say abou he velociy of he car over ime? a) i speeds up all he ime b) i slows down all he ime c) i moves a consan velociy d) someimes i speeds up and someimes i slows down e) no really sure x

24 Quesion 2.13b Graphing Velociy II The graph of posiion vs. ime for a car is given below. Wha can you say abou he velociy of he car over ime? a) i speeds up all he ime b) i slows down all he ime c) i moves a consan velociy d) someimes i speeds up and someimes i slows down e) no really sure The car slows down all he ime because he slope of he x vs. graph is diminishing as ime goes on. Remember ha he slope of x vs. is he velociy! A large, he value of he posiion x does no change, indicaing ha he car mus be a res. x

25 Quesion 2.14a v versus graphs I a) decreases Consider he line labeled A in b) increases he v vs. plo. How does he c) says consan speed change wih ime for d) increases, hen decreases line A? e) decreases, hen increases v A B

26 Quesion 2.14a v versus graphs I a) decreases Consider he line labeled A in he v vs. plo. How does he speed change wih ime for line A? b) increases c) says consan d) increases, hen decreases e) decreases, hen increases v A B In case A, he iniial velociy is posiive and he magniude of he velociy coninues o increase wih ime.

27 Quesion 2.14b v versus graphs II Consider he line labeled B in he v vs. plo. How does he speed change wih ime for line B? a) decreases b) increases c) says consan d) increases, hen decreases e) decreases, hen increases v A B

28 Quesion 2.14b v versus graphs II Consider he line labeled B in he v vs. plo. How does he speed change wih ime for line B? a) decreases b) increases c) says consan d) increases, hen decreases e) decreases, hen increases v A B In case B, he iniial velociy is posiive bu he magniude of he velociy decreases oward zero. Afer his, he magniude increases again, bu becomes negaive, indicaing ha he objec has changed direcion.

29 2-5 Moion wih Consan Acceleraion If he acceleraion is consan, he velociy changes linearly: Average velociy: (2-7) Noe: valid only for consan acceleraion

30 2-5 Moion wih Consan Acceleraion Average velociy: (2-9) Posiion as a funcion of ime: x = x0 + vav (2-10) (2-11) Velociy as a funcion of posiion: v v a = + 0 (2-12)

31 2-5 Moion wih Consan Acceleraion The relaionship beween posiion and ime follows a characerisic curve.