Midterm ExamStudy of MotionStudy of MotionStudy of MotionSpeedDistance equationExample of speed calculationCommon units of speedSpeed of cheetahCar travelingAccelerationExamples of accelerationRate of change of speedRate of change of speedRate of change of speedRate of change of speedAccelerationAcceleration of GravityAcceleration of GravityProblemsSolution 1Solution 2Solution 3AccelerationDistanceDistance TraveledProblemEquationsCat’s jump—how fast?Cat’s jump—how far?Midterm Exam•100-90%A 5•89-80% B 12•79-70% C 15•69-60% D 13•59% or less F• High score 70 out of 76• Every score divided by 70 for the percent marked on your exam. Average is 72%.• You can raise your score by doing Part I problems outside class and turning it in at the beginning of class on Tuesday, February 21: on separate page, turn in both original and new work—go see a tutor!!• If you feel I marked an answer wrong in error, see me in my office during office hours, with documentation of correct answerStudy of Motion• Aristotle– Tutor of Alexander– Student of Plato– Ignored friction– Motion ceased when objects in their proper place– Influential for 2000 yearsStudy of Motion• Galileo– Studied Copernicus’ work of 1543– Defined ‘inertia’: keep moving in same direction and speed without outside influences– Noted that gravity increased speed of falling objects, decrease speed of rising objects• 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=• hhkm1060km240km600Accelerationinterval Timeyin velocit Change=onAcceleratiCHANGE of speed over time, not the RATE of speed• RATE OF CHANGEExamples of acceleration• Driving on Monmouth Avenue• 20 mi./h• Increase to 45 mi./h in 25 seconds—change in speed is:• Divide by time to change speed=−hmihmi .20.45hmi.25shmishmi⋅= /.125/.25Rate of change of speedFind how much you change, then divide by amount of time over which the change occurs=−hmihmi .20.45hmi.25shmishmi⋅= /.125/.25Rate of change of speed• Car can go from stopped to 90 km/h in 10 seconds•Be sure to REDUCEto lowest termsshkmshkm⋅= /910/90Rate of change of speed• Car goes from 60 km/h to 65 km/h in 2.5 seconds• First find amount of changeshkmshkm⋅= /25.2/5Rate of change of speed• Bicycle goes from rest to 5 km/h in 2.5 secondsshkmshkm⋅= /25.2/5Acceleration• Neglect air resistance for these equationsa=v/t Æ v=at• acceleration is velocity divided by time• velocity acquired is acceleration multiplied by time• 9.8 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 1atv =2/10 sma =st 5.3=ssmv 5.3)10(2=smv /35=Solution 2atv =2/10 sma =st 6=smv /60=ssmv 6)10(2=Solution 3atv =2/10 sma =st 100=smv /1000=ssmv 100)10(2=Acceleration• Rate of increase of a rated/tt• Increases rate for each increment in time that has passed• So there is an increased of 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 mProblem• 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 =Equations•How fast?•How far?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
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