Linear MotionStudy of MotionStudy of MotionGalileo’s investigation of motionGalileo’s investigation of motionGalileo’s inclined planesGalileo’s inclined planesStudy of MotionSpeedDistance equationExample of speed calculationCommon units of speedSpeed of cheetahCar travelingSpeed and VelocityAccelerationExamples of accelerationRate of change of speedRate of change of speedRate of change of speedRate of change of speedGalileo’s Inclined PlanesAccelerationAcceleration of GravityAcceleration of GravityProblemsSolution aSolution bSolution cAccelerationDistanceDistance TraveledEquationsUNITS in EquationsProblemCat’s jump—how fast?Cat’s jump—how far?Acceleration of GravityAcceleration of GravityHang time for basketball playerLinear MotionSupplemental Textbook Materials Chapter 12: Pages 262-276Review Questions 4, 7, 8, 10, 11, 15, 16, 17Study of Motion• Aristotle– Student of Plato– Tutor of Alexander– Motion ceased when objects in their proper place– Thought speed depended on weight– Ignored friction, air resistance– Influential for 2000 yearsStudy of Motion• Galileo– Studied Copernicus’work of 1543– Speed not dependent on weight, only on amount of time for fallingGalileo’s investigation of motion– Speed not dependent on weight, only on amount of time for falling– Noted that gravity increased speed of falling objects, decrease speed of rising objects– Defined ‘inertia’: keep moving in same direction and speed without outside influences• Surface area changes air resistance• Objects reach terminal velocity due to air resistance• In vacuum, this is not a factorGalileo’s investigation of motionGalileo’s inclined planes• Balls roll down faster and faster• Roll up slower and slower• Rises to same height as it is released• Height not dependent on inclineGalileo’s inclined planes• Speed—how fast • Velocity—how fast and what direction• Acceleration—how fast it is changing how fastStudy of MotionSpeedtimespeeddistance==hkm4320h80kmDistance equationdistance timeRate=ו Keep units with numbers, so you know you have set up the problems correctlyExample of speed calculationkmhhkm320480=•• Notice that hours cancels because it is above and below the fraction barCommon units of speed• Miles per hour mph mi./h• Kilometers per hour km/h• Meters per second m/sSpeed of cheetahsm4100sm250sm/25Car traveling• 60 km/h for 4 h• 60 km/h for 10 h=• hhkm460=• hhkm1060km240km600Speed and VelocityAccelerationinterval Timeyin velocit ChangeonAccelerati• =CHANGE of speed over time, not the RATE of speed• RATE OF CHANGEExamples of acceleration• Driving on Monmouth Avenue at 20 mi./h• Increase to 45 mi./h in 25 seconds—change in speed is:• Divide change of speed by timeand=−hmihmi .20.45smhmi 2.11.25=shmishmia ⋅== /.125/.25hmi.25244.025/2.11smssma ==Rate of change of speedFind how much you change, Δ vThen divide by amount of time over which the change occurs=−hmihmi .20.45hmi.25shmishmia ⋅== /.125/.25244.025/2.11smssma ==Rate of change of speed• Car can go from stopped to 90 km/h in 10 seconds•Be sure to REDUCEto lowest termsshkm10/90shkm⋅=/9smhrkm 2590=25.210/25smssm=Rate of change of speed• Car goes from 60 km/h to 65 km/h in 2.5 seconds• First find amount of change• Then divide by timeshkmshkm⋅= /25.2/5smhrkm 39.15=255.05.2/39.1smssm=Rate of change of speed• Bicycle goes from rest to 5 km/h in 2.5 secondsshkmshkm⋅= /25.2/5255.05.2/39.1smssm=Galileo’s Inclined Planes• Acceleration same for each second of travel• Picks up speed faster on steeper inclines• Free falling objectsAcceleration• Neglect air resistance for these equationsa=v/t Æ v=at• acceleration is velocity divided by time• velocity acquired is acceleration multiplied by time• 9.83 m/s2• Round off to 10 m/s2Acceleration of GravityAcceleration of Gravity• Free fall of object• Speed increases 10 m/s for every second of fall• 10 m/s= 10mss2Time elapsed(seconds)Speed (meters/ second)00 110220330440Problems• If a rock is rock is pried loose from a cliff (by frost wedging) what is its speed 3.5 seconds after it starts falling?• After 6 seconds?• After 100 seconds?Solution agtv =2/10 smg =st 5.3=ssmv 5.3)10(2=smv /35=Solution bgtv =2/10 smg =st 6=smv /60=ssmv 6)10(2=Solution cgtv =2/10 smg =st 100=smv /1000=ssmv 100)10(2=hmihkmv /2236/3600==Acceleration• Rate of increase (or decrease) of a rated/tt• Changes rate for each increment in time that has passed• So there is an increased (or decreased) distance for each successive time intervalDistance• g= acceleration of gravity (a)= 10m/s2• t lower case for time• (T upper case means Temperature)221gtd =22)10(21tsmd =Distance TraveledTime elapsedSpeed00 m/s110 m/s220 m/s330 m/s440 m/sDistance traveled in 1 second05 m15 m25 m35 mTotal Distance traveled0 m5 m20 m45 m80 mEquations•How fast?– Know distance and time, use:– Know acceleration and time, use:•How far?– Know velocity and time, use:– Know acceleration and time, use:atv =221atd =vtd=tdv =gtv=221gtd =UNITS in Equations• How fast? Velocity• How far? accelerationsmsssmssmatv =×⋅=×==12mssmatd =⋅⋅==12121222mssmvtd =×==smtdv ==Problem• Cat steps off ledge and reaches ground after ½ second.• How fast was she going when she touched the ground?• What is the height of the ledge?gtv=221gtd =Cat’s jump—how fast?ssmv 5.0)10(2=smssmv /55.0)10(2==Cat’s jump—how far?22)5.0)(10(21ssmd =mssmd 25.1)5.0)(10(2122==Acceleration of Gravity• Gains speed for each interval of time that object is falling• Loses speed for each interval of time it rises on an upward throw• Gains at same rate on its downward pathAcceleration of GravityHang time for basketball player• Spud Webb slam dunk contest• He can jump 1.25 m. How long is he in the air?→to go up, so double for time in the airgdt2=• http://www.youtube.com/watch?v=BUu7drj9hPw221gtd =ssmmgdt
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