# Displacement, Velocity, and Acceleration. (WHERE and WHEN?)

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1 Dsplacemen, Velocy, and Acceleraon (WHERE and WHEN?)

2 Mah resources Append A n your book! Symbols and meanng Algebra Geomery (olumes, ec.) Trgonomery Append A Logarhms

3 Remnder You wll do well n hs class by PRACTICING! Era Pracce Problems: 2.1, 2.3, 2.5, 2.21, 2.25, 2.27 Also: (Ungraded) homework warm-up problems

4 Remnders Ne class s ne Wednesday. Problem solng day: praccng or eam. Frs clcker grade couned; BRING YOUR CLICKERS!

5 Problem Solng Pro-ps 1. Draw a pcure! 2. Use and label your reerence rame. 3. Ls wha you KNOW and DON T KNOW n arable orm. 4. Pracce helps you pck bes ormulas!

6 Scalars and Vecors Scalar: jus a number (magnude). Vecor: a number (magnude) wh a drecon.

7 Scalars and Vecors Scalar: jus a number (magnude). Vecor: a number (magnude) wh a drecon. 100 m 30 m

8 Scalars and Vecors Scalar: jus a number (magnude). Vecor: a number (magnude) wh a drecon. 100 m 30 m Dsance (scalar): 100m + 30m 130 meers

9 Scalars and Vecors Scalar: jus a number (magnude). Vecor: a number (magnude) wh a drecon. Dsplacemen, (ecor): meers Inal locaon 100 m Fnal locaon 30 m Dsance (scalar): 100m + 30m 130 meers

10 Scalars and Vecors Scalars: Vecors: Dsance, Speed, Dsplacemen, Velocy, Acceleraon, a Vecors are usually represened as BOLD (or wh an arrow ha).

11 Frames o reerence 80 km/h +10 km/h 70 km/h Ground s reerence rame Velocy, Drer s reerence rame In ground rame o reerence, one car has +80 km/h whle he oher has +70 km/h In reerence rame o drer, elocy o oher car s +10 km/h

12 Reerence rames on paper PT #1: Draw a pcure! Jogger wen 10m eas, 10m norh, sa on a sump a whle, hen walked 25m eas.

13 Reerence rames on paper PT #1: Draw a pcure! Jogger wen 10m eas, 10m norh, sa on a sump a whle, hen walked 25m eas.

14 Reerence rames on paper PT #1: Draw a pcure! PT #2: Use (and LABEL) a coordnae sysem. Jogger wen 10m eas, 10m norh, sa on a sump a whle, hen walked 25m eas y + -y

15 Reerence rames on paper PT #1: Draw a pcure! PT #2: Use (and LABEL) a coordnae sysem. Jogger wen 10m eas, 10m norh, sa on a sump a whle, hen walked 25m eas y + -y The drecon o hese arrows s mporan or seng up problems and may aec he sgn o your arables and/or answers (wll see eample soon)

16 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ

17 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car.

18 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps!

19 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! Fnal poson Inal poson

20 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! +y Fnal poson Inal poson +

21 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! Fnal poson +y Pro Tp #3: Ls wha you know & don known n arable orm Inal poson +

22 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! Fnal poson +y Pro Tp #3: Ls wha you know & don known n arable orm Inal poson +3.0 m +

23 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! Fnal poson +y Pro Tp #3: Ls wha you know & don known n arable orm Inal poson -5.0 m +3.0 m +

24 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Ths one s easy, bu le s pracce pro ps! Fnal poson +y Pro Tp #3: Ls wha you know & don known n arable orm Inal poson -5.0 m +3.0 m + Δ?

25 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. +y Fnal poson Inal poson -5.0 m +3.0 m + Δ -5.0 m - (+3.0 m) -8.0 m

26 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. +y Fnal poson Inal poson Δ -8.0 m + Arrow represens he Δ ecor: magnude (8.0m) and drecon (-) o dsplacemen.

27 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. +y Fnal poson Inal poson +

28 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Fnal poson Inal poson + +y Wre your knowns and unknowns!

29 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Fnal poson Inal poson + +y Wre your knowns and unknowns!

30 Dsplacemen (ecor) Denon: change n he poson o an objec Dsplacemen: Δ E: Car nally parked 3.0 m o rgh o house, dres around he block, ends up 5.0 m o le o house. Fnd he dsplacemen o he car. Fnal poson Inal poson m +y -3.0 m Δ +5.0 m - (-3.0 m) +8.0 m

31 Many people sruggle wh sgns! Ask yoursel aer denng each arable: Is he sgn conssen wh wha drecon I e called pose? Up and rgh are usually pose! (parcularly n WebAssgn unless eplcly saed n he problem)

32 Aerage Velocy Denon: elocy s dsplacemen per un me Δ SI uns: m/s Δ

33 Aerage Velocy Denon: elocy s dsplacemen per un me Δ SI uns: m/s Δ E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang

34 Aerage Velocy Denon: elocy s dsplacemen per un me Δ SI uns: m/s Δ E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy gong o P: Mo own P 0 70 m 2 hrs

35 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy gong o P: Mo own P 70 m 2 hrs

36 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy gong o P: m 2 hrs 0 Mo own P 70 m 2 hrs

37 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy gong o P: m 2 hrs 0 Mo own P 70 m 2 hrs 70 m m/hr 2 hrs 0

38 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy gong o P: m 2 hrs 0 Mo own P 70 m 2 hrs 70 m m/hr 2 hrs 0

39 Aerage Velocy Denon: elocy s dsplacemen per un me Δ SI uns: m/s Δ E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy comng back rom P? Aerage elocy o round rp? I you nsh hose: Aerage speed (scalar!) o round rp?

40 Aerage Velocy Denon: elocy s dsplacemen per un me Δ SI uns: m/s Δ Speed: 140m / 3h 47 m / h!

41 Speed: 140m / 3h 47 m / h! Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang

42 Speed: 140m / 3h 47 m / h! Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy comng back rom P:

43 Speed: 140m / 3h 47 m / h! Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy comng back rom P: 0 70 m 3 hrs 2 hrs 70 m/hr

44 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Aerage elocy comng back rom P: 0 70 m 3 hrs 2 hrs 70 m/hr Aerage elocy o round rp: Speed: 140m / 3h 47 m / h!

45 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Mo own P Aerage elocy comng back rom P: Aerage elocy o round rp: 0 70 m 0 3 hrs hrs 70 m 0 2 hrs Speed: 140m / 3h 47 m / h! 0 70 m/hr

46 Aerage Velocy Denon: elocy s dsplacemen per un me Δ Δ SI uns: m/s E: Go o Psburgh n 2 hrs, back n Morganown 3 hrs aer leang Mo own P Aerage elocy comng back rom P: Aerage elocy o round rp: 0 70 m 0 3 hrs hrs 70 m 0 2 hrs Speed: 140m / 3h 47 m / h! 0 70 m/hr

47 Insananeous Velocy Insananeous elocy s elocy a a parcular nsan. Only use he aerage elocy when asked or aerage.

48 Insananeous Velocy Insananeous elocy s elocy a a parcular nsan. Only use he aerage elocy when asked or aerage.

49 Insananeous Velocy Insananeous elocy s elocy a a parcular nsan. Only use he aerage elocy when asked or aerage. Wll dscuss hs derence more ne lecure.

50 Acceleraon Aerage acceleraon change n elocy/me a Δ Δ Insananeous acceleraon Δ a lm Δ 0 Δ SI Uns: m/s/s m/s 2

51 Acceleraon Aerage acceleraon change n elocy/me a Δ Δ Insananeous acceleraon Δ a lm Δ 0 Δ SI Uns: m/s/s m/s 2 The sgn o acceleraon ndcaes whch drecon s elocy changes. Pose acceleraon means speedng up when mong n he pose drecon OR slowng down when mong n he negae drecon.

52 Sgns o acceleraon A car slowng down a a sop sgn a A bulle hng a wall + a + Sprner ou o he blocks a +

53 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o locaon a me zero elocy a me zero a me zero

54 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a

55 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o

56 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o

57 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag

58 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o

59 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o o + ag

60 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o o + ag ag + 2 o

61 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o o + ag Smlar deraons lead o more equaons: ag + 2 o

62 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o o + ag Smlar deraons lead o more equaons: ag + 2 o Δ + o 1 a 2 2

63 Moon a Consan Acceleraon Specal case when a does no change wh me Noaon: 0 o o a me zero locaon a me zero elocy a me zero a a o + a o ag ag o o + ag Smlar deraons lead o more equaons: ag + 2 o Δ + o 1 a o + 2aΔ

64 Whch ormula o use? ag 2 o

65 Whch ormula o use? a o + o + 2aΔ 2 2 ag 2 o Δ o + 1 a 2 2

66 Whch ormula o use? a o + o + 2aΔ 2 2 ag 2 o Δ o + 1 a 2 2 Pro Tp #3: Ls wha you know and need o know n arable orm

67 Whch ormula o use? a o + o + 2aΔ 2 2 ag 2 o Δ o + 1 a 2 2 Pro Tp #3: Ls wha you know and need o know n arable orm 1 equaon wh one unknown s solable.

68 Whch ormula o use? a o + o + 2aΔ 2 2 ag 2 o Δ o + 1 a 2 2 Pro Tp #3: Ls wha you know and need o know n arable orm 1 equaon wh one unknown s solable. 2 equaons wh wo unknowns s solable.

69 Whch ormula o use? a o + o + 2aΔ 2 2 ag 2 o Δ o + 1 a 2 2 Pro Tp #3: Ls wha you know and need o know n arable orm 1 equaon wh one unknown s solable. 2 equaons wh wo unknowns s solable. Pro Tp # 4: Pracce helps you pck bes ormulas!

70 Le s Pracce! The speed o a nere mpulse n he human body s abou 100 m/s. I you accdenally sub your oe n he dark, esmae he me akes he nere mpulse o rael o your bran.

71 Le s Pracce! The speed o a nere mpulse n he human body s abou 100 m/s. I you accdenally sub your oe n he dark, esmae he me akes he nere mpulse o rael o your bran. Draw a pcure and ls knowns and unknowns

72 Le s Pracce! The speed o a nere mpulse n he human body s abou 100 m/s. I you accdenally sub your oe n he dark, esmae he me akes he nere mpulse o rael o your bran. Draw a pcure and ls knowns and unknowns Aerage elocy 100 m/s dsplacemen / me

73 Le s Pracce! The speed o a nere mpulse n he human body s abou 100 m/s. I you accdenally sub your oe n he dark, esmae he me akes he nere mpulse o rael o your bran. Draw a pcure and ls knowns and unknowns Aerage elocy 100 m/s dsplacemen / me Change n me Δ Δ/ ~2 m / 100 m/s

74 Le s Pracce! The speed o a nere mpulse n he human body s abou 100 m/s. I you accdenally sub your oe n he dark, esmae he me akes he nere mpulse o rael o your bran. Draw a pcure and ls knowns and unknowns Aerage elocy 100 m/s dsplacemen / me Change n me Δ Δ/ ~2 m / 100 m/s 0.02 s or 20 mllseconds

75 Problems nsde problems Mgh need o break down problem no smaller peces! Sole n sequence.

76 Le s Pracce! 1 mle 1609 m

77 Le s Pracce! A rocke shp s capable o accelerang a a rae o 0.60 m/s 2. How long does ake or o ge rom gong 55 m/h o gong 60 m/h? 1 mle 1609 m

78 Le s Pracce! A rocke shp s capable o accelerang a a rae o 0.60 m/s 2. How long does ake or o ge rom gong 55 m/h o gong 60 m/h? Draw a pcure and ls knowns and unknowns 1 mle 1609 m

79 Le s Pracce! A rocke shp s capable o accelerang a a rae o 0.60 m/s 2. How long does ake or o ge rom gong 55 m/h o gong 60 m/h? Draw a pcure and ls knowns and unknowns Wan: Δ Know: o,, a 1 mle 1609 m

80 Le s Pracce! A rocke shp s capable o accelerang a a rae o 0.60 m/s 2. How long does ake or o ge rom gong 55 m/h o gong 60 m/h? Draw a pcure and ls knowns and unknowns Wan: Δ Know: o,, a o +a Δ rearrange: Δ (- o )/a 1 mle 1609 m

81 Le s Pracce! A rocke shp s capable o accelerang a a rae o 0.60 m/s 2. How long does ake or o ge rom gong 55 m/h o gong 60 m/h? Draw a pcure and ls knowns and unknowns Wan: Δ Know: o,, a o +a Δ rearrange: Δ (- o )/a Wll need o coner m/h o wha? 1 mle 1609 m

82 Whle chasng s prey n a shor sprn, a cheeah sars rom res and runs 45 m n a sragh lne, reachng a nal speed o 72 km/h. (a) Deermne he cheeah s aerage acceleraon durng he shor sprn, and (b) nd s dsplacemen a 3.5s.

83 Problem Solng Pro-ps 1. Draw a pcure! 2. Use and label your reerence rame. 3. Ls wha you KNOW and DON T KNOW n arable orm. 4. Pracce helps you pck bes ormulas!

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