PHYS 1441 – Section 002 Lecture #4AnnouncementsSlide 3Reminder: Special Problems for Extra CreditDisplacement, Velocity and SpeedExample 2.1Example Distance Run by a JoggerExample: The World’s Fastest Jet-Engine CarInstantaneous Velocity and SpeedPosition vs Time PlotSlide 11Velocity vs Time PlotSlide 13AccelerationAcceleration vs Time PlotExample 2.3Few Confusing Things on AccelerationOne Dimensional MotionOne Dimensional Motion cont’dKinematic Equations of Motion on a Straight Line Under Constant AccelerationWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu1PHYS 1441 – Section 002Lecture #4Wednesday, Sept. 15, 2010Dr. Jaehoon Yu•One Dimensional Motion•Instantaneous Velocity and Speed•Acceleration•Motion under constant acceleration•One dimensional Kinematic Equations•How do we solve kinematic problems?•Falling motionsAnnouncements•E-mail subscription–A test message was sent out yesterday!•Thanks for your replies!•If you haven’t yet, please check your e-mail and reply ONLY TO ME!–66/80 subscribed! Please subscribe ASAP•1st term exam–Non-comprehensive –Time: 1 – 2:20pm, Wednesday, Sept. 22–Coverage: Appendices A.1 – A.8 and CH1.1 – what we finish coming Monday, Sept. 20•Quiz results–Class average: 8.3/16•Equivalent to 52/100–Top score: 16/16•Colloquium at 4pm today in SH101–Physics faculty research expo!!Wednesday, Sept. 15, 20102PHYS 1441-002, Fall 2010 Dr. Jaehoon YuWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu4Reminder: Special Problems for Extra Credit•Derive the quadratic equation for yx2-zx+v=0 5 points•Derive the kinematic equation from first principles and the known kinematic equations 10 points•You must show your OWN work in detail to obtain the full credit•Must be in much more detail than in pg. 19 of this lecture note!!!•Due Monday, Sept. 27( )2 20 02v v a x x= + -Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu5Displacement, Velocity and SpeedOne dimensional displacement is defined as: ixxx f The average velocity is defined as: xv �The average speed is defined as: Total Distance TraveledTotal Elapsed Timev �ffiix xt t-=-xtDDDisplacement per unit time in the period throughout the motionDisplacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance?DisplacementElapsed Time�Unit?m/sUnit?mUnit?m/sWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu6Example 2.12 1fix x x x xD � - = -•Displacement: •Average Velocity: ffixix xvt t-�-•Average Speed: Total Distance TraveledTotal Time Intervalv �The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x1=50.0m to x2=30.5 m, as shown in the figure. What was the runner’s average velocity? What was the average speed?30.5 50.0= -19.5( )m=-2 12 1x x xt t t- D= =- D19.56.50( / )3.00m s-= =-50.0 30.5 19.56.50( / )3.00 3.00m s- += = =+Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu7How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m/s?Average speed =Distance =Example Distance Run by a JoggerDistance Elapsed time( ) ( )Average speed Elapsed time =( )2.22 m s=( )5400 s =12000 mWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu8Andy Green in the car ThrustSSC set a world record of 341.1 m/s in 1997. To establish such a record, the driver makes two runs through the course, one in each direction to nullify wind effects. From the data, determine the average velocity for each run.Example: The World’s Fastest Jet-Engine Car=vrtD=Dxr =1609 m+339.5m s+4.740 s=vrtD=Dxr =1609 m-342.7 m s-4.695 sWhat is the speed?What is the speed?v = =vrv = =vr339.5m s342.7 m s-342.7 m s=Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu9Instantaneous Velocity and Speed•Can average quantities tell you the detailed story of the whole motion?xxvt�D=DΔt 0lim*Magnitude of Vectors are Expressed in absolute values•Instantaneous speed is the size (magnitude) of the velocity vector:xxvt�D=DΔt 0lim•Instantaneous velocity is defined as:–What does this mean?•Displacement in an infinitesimal time interval•Average velocity over a very short amount of timeNO!!Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu10Position vs Time Plottimet1t2t3t=0Positionx=0x112 31. Running at a constant velocity (go from x=0 to x=x1 in t1, Displacement is + x1 in t1 time interval)2. Velocity is 0 (go from x1 to x1 no matter how much time changes)3. Running at a constant velocity but in the reverse direction as 1. (go from x1 to x=0 in t3-t2 time interval, Displacement is - x1 in t3-t2 time interval)It is useful to understand motions to draw them on position vs time plots.Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu11Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu12Velocity vs Time PlotWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu13Displacement, Velocity and Speedxxvt�D=DΔt 0limDisplacementixxxfAverage velocitytxttxxviixffAverage speedSpent Time TotalTraveled Distance TotalvInstantaneous velocityInstantaneous speedxxvt�D=DΔt 0limWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu14Accelerationxa �xv �analogs toxa �xxvt�D�DΔt 0limanalogs toChange of velocity in time (what kind of quantity is this?)•Average acceleration:•Instantaneous acceleration: Average acceleration over a very short amount of time.xffxiiv vt t-=-xvtDDffiix xt t-=-xtDDxvt�DDΔt 0limVector!Unit?m/s2Dimension?[LT-2]Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu15Acceleration vs Time PlotWhat does this plot tell you?Yes, you are right!!The acceleration of this motion is a constant!!Wednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu16Example 2.3xa =)/(2.40.5210.50212smA car accelerates along a straight road from rest to 75km/h in 5.0s.What is the magnitude of its average acceleration?xfv =xiv = )/(105.4100036002.4242hkm0 /m s750003600ms=21 /m sxf xif iv vt t-=-xvtDDWednesday, Sept. 15, 2010PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu17Few Confusing Things on Acceleration•When an object is moving in a constant velocity (v=v0), there is no
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