Speed and Velocity distance travelled speed = elapsed time average velocity v av
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1 : One-Dimensional Kinemaics Kinemaics: he sudy of moion Posiion, Disance and Displacemen Needed: 1 coordinae sysem ( posiion is relaie ) ofen chosen wih a conenien origin Disance = oal lengh of rael s. Displacemen = change in posiion = final posiion - iniial posiion = f - i Eample Consider arious rips and he corresponding disances/displacmens = D FH YH RWM.1mi 4.3mi p5c:1
2 Speed and Velociy disance raelled speed = elapsed ime aerage elociy a = elociy =rae of change of displacemen =slope of displacemen s ime graph =lim hp://phys3p.sl.psu.edu/~mrg3/mahanim/calc_i/calc_i.hml angen and angens animaions noe:aerage elociy equals insananeous elociy if elociy is consan Aciiy 1: moion sensor fun displacemen ime D D Aciiy : slope apple: graphical inerpreaion of raes of change hp://phys3p.sl.psu.edu/simulaions/physles/csp7_pcsimulaion.hml p5c:
3 insananeous elociy = slope of displacemen ersus-ime graph displacemen = area under he cure of elociy-ime graph s s = s = s 1 + s = + 1 D 1 + D s s 1D1 D 3D3 1 D 1 D D D 1 D 3 p5c:3
4 acceleraion: rae of change of elociy changes in speed as well as direcion of rael aerage elociy: he raio of he displacemen during a ime ineral o he lengh if he ime ineral a a =aerage acceleraion= 1 = 1 Graphical Inerpreaion of acceleraion Acceleraion is he slope of he graph of elociy ersus ime may be posiie or negaie (direcion!) Insananeous Acceleraion is he slope elociy ime D D aerage acceleraion equals insananeous acceleraion if acceleraion is consan insananeous acceleraion = slope of elociy ersus-ime graph elociy = area under he cure of acceleraion-ime graph! p5c:4
5 p5c:5 Moion wih Consan Acceleraion consan acceleraion slope of elociy-ime graph is sraigh line aerage elociy: w/ subsiuion and some algebra The Fab Four ) ( a and - - = +a ) ( 1 ) ( 1 a a a - a = = a =
6 Problem Soling Tips Draw a diagram Wrie down all known quaniies, idenify on diagram. Wrie down all unknown quaniies, idenify on diagram. Find basic equaion which relaes each unknown quaniy o known quaniies. Sole equaion for he desired unknown. plug and chug p5c:6
7 Eample: A ferry makes a shor run beween wo docks wih a cruising speed of 7.4 m/s. If he ferry mus come o sop in 1.3 s, wha is is aerage acceleraion? How far does i rael before coming o res? Eample: A ball is hrown sraigh up wih an iniial speed of 8. m/s. If he ball has an acceleraion of 9.81 m/s downwards, wha is is elociy afer.5 s and afer 1 s? p5c:7
8 Eample: An dragser acceleraes a he rae of 7.4 m/s. How far is i from is saring poin afer 1.,. and 3.s? How fas is i going a hese imes? Eample: An aircraf mus accelerae from res o akeoff speed wihin he lengh of he runway. Find an epression which relaes he minimum lengh of runway o he aircraf's acceleraion a and akeoff speed o. How long a runway is required if he aircraf's acceleraion is. m/s and ake off speed is 95. m/s. p5c:8
9 Eample: A drier cruising a 11.4 m/s spos a deer in his headlighs and immediaely his his brakes, slowing wih a deceleraion of 3.8 m/s. If he deer is. m from he car when he brakes are applied, who close is he dear o being hi? How much ime does i ake he car o come o a res? Eample: A car doing 4. mph (17.9 m/s) in a 5 mph passes a parked police car. The insan he obliious drier passes he police car, he police car ses off in pursui wih an acceleraion of 4.5 m/s. How long does i ake he officer o cach up wih he scofflaw? How far hae he wo ehicles raeled in his ime? Wha is he final speed of he police car when i has caugh up o he offending ehicle. p5c:9
10 Acceleraion of Graiy Hisorical Perspecie: Aemps o describe moion by Galileo Eperimen and obseraion as he foundaion of science ramps and freefall idealizaions and simplificaions: ignoring air resisance g = 9.81 m/s (9.78 a equaor, 9.83 a poles) = 3 f/s a = g, acceleraion is direced downwards (wach direcions in problems!!!) p5c:1
11 Eample: A person seps of he end of a 3. m high diing board and drops ino he waer below. How much hang ime does he person ge? Wha is he person's speed upon enering he waer? Eample: A olcano shoos blobs of molen laa(laa bombs) sraigh ino he air. A nearby geologis noes ha hey are in he air for 4.75s before hiing he ground agian. Assuming freefall, wha are he iniial speeds of he laa bombs? Wha is heir maimum heigh? p5c:11
12 Eample: A ho air balloon rising sraigh ino he air wih a consan speed of 6.5 m/s loses one of is ballas bags dislodges when he balloon is a a heigh of. m. How long is he sandbag in he air before i his he ground? Wha is he greaes heigh of he sandbag once i is released? p5c:1
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