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The displacement (in centimeters) of a particle moving

Calculus: Early Transcendentals | 6th Edition | ISBN: 9780495011668 | Authors: James Stewart ISBN: 9780495011668 184

Solution for problem 2.11 Chapter 2

Calculus: Early Transcendentals | 6th Edition

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Calculus: Early Transcendentals | 6th Edition | ISBN: 9780495011668 | Authors: James Stewart

Calculus: Early Transcendentals | 6th Edition

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Problem 2.11

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion , where is measured in seconds. (a) Find the average velocity during each time period: (i) [1, 2] (ii) [1, 1.1] (iii) [1, 1.01] (iv) [1, 1.001] (b) Estimate the instantaneous velocity of the particle when

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WesleyFowler ASTR Chapter11 Jupiter th SemimajorAxisis5.2AU(5 planetfromtheSun) OrbitalPeriodis11.86years Jupiterhas67knownmoons Hasthreerings(allgasgiantshaverings) Synodicperiodis398.9days 4 brightestobjectinEarth’ssky MeanRadius:69,900km(~11Earthswide) – EquatorialRadius:71,492km(11.21E.Radii) – PolarRadius:66,854km(10.52E.Radii) 27 Mass:1.9x10 kg(318EarthMasses) 3 AverageDensity:1,300kg/m 2 SurfaceGravity:24.8m/s (2.53g) JupiterhasthefastestrotationintheSolarSystem,makingacompleterotationin10hours. Jupiterhasadifferentiatedrotation,asinthatithasdifferentrotationratesatdifferent latitudes.Thisistrueforallgasgiants RotationalPeriod: Equatorial:9hrs50min Polar:9hrs55min MagneticField:9hrs55min Jupiterhasadifferentialradius,shapedasan OblateSpheriod.Thisiscausedbytheplanet’s veryfastrotationrate. Jupiterhasanatmosphere,andamagnetic fieldthatis20,000timesstrongerthanEarth’s Composition: Hydrogen(H ):26.1% Helium(He):13.8% HeavierElements:0.1% - Representstheprimarycompositionoftheentireuniverse,andourancientsolarnebula Jupiter’sSurfaceFeatures Bandedstructureofbrightzones,anddarkreddishbelts - Thezonalflowofeachbandisdeterminedbyeastwardandwestwardwind DarkBelts:Eastwardflow - Brownish-red - High-pressure,loweraltitude LightZones:Westwardflow - Whitish - Low-pressure,highaltitude Storms:Comeinwhiteovals,redspots,and brownovals - TheGreatRedSpotisahurricanelikestorm,andcancanfitthreeEarth’sinsideit.Was firstobserved300yearsago.Currentlyshrinking. - BrownOvalsareholesintheatmosphere,revealingthedeepestlayersofJupiter Stratosphere:(Belowthe“surface”) Troposphere(Abovethe“surface”) - Top:AmmoniaIceClouds[-40km] - Mid[-60km]:Ammoniumhydrosulfideice[maybetheredcoloringagent] - Bottom[-80km]:WaterIce(toodeeptosee) Jupiterhasitsowninternalheatsourceleftoverfromitsformation. - ItissohotbelowJupiter’s“surface”thathydrogenexistspurelyasaliquid - Liquidmetallichydrogen:Hydrogenbecomesanexcellentconductorofelectricityasit beginstoliquidateandbehavemorelikeametal.Beinghighlyconvective,themantle createsanimmenselystrongdynamoeffect,andthusamassiveelectromagneticfield. - Underneaththeliquidmetallichydrogeniswhatisbelievedtobearockycore(20,000K)

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Textbook: Calculus: Early Transcendentals
Edition: 6
Author: James Stewart
ISBN: 9780495011668

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