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