PHYS 1441 – Section 501 Lecture #2AnnouncementsDisplacement, Velocity and SpeedDifference between Speed and VelocityExample 2.1Instantaneous Velocity and SpeedPosition vs Time PlotVelocity vs Time PlotSlide 9AccelerationAcceleration vs Time PlotExample 2.4Meanings of AccelerationOne Dimensional MotionOne Dimensional Motion cont’dKinematic Equations of Motion on a Straight Line Under Constant AccelerationHow do we solve a problem using a kinematic formula for constant acceleration?Example 2.10Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu1PHYS 1441 – Section 501Lecture #2Monday, June 7, 2004Dr. Jaehoon YuRemember the quiz this Wednesday!!•Chapter two: Motion in one dimension–Velocity (Average and Instantaneous)–Acceleration (Average and instantaneous)–One dimensional motion at constant acceleration•Free Fall–Coordinate systemsMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu2Announcements•Reading assignment #1: Read and follow through all sections in appendix A by Wednesday, June 9–A-1 through A-9•There will be a quiz on this Wednesday, June 9, on these and Chapter 1•E-mail distribution list: 16 of you have registered–Remember 5 (3) extra credit points if done by midnight tonight (Wednesday).•Homework: You are supposed to download the homework assignment, solve it offline and input the answers back online.–38 registered–25 submitted–Must be submitted by 6pm Wednesday to get full, free credit.Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu3Displacement, Velocity and SpeedOne dimensional displacement is defined as: Displacement is the difference between initial and final potions of motion and is a vector quantityixxxfAverage velocity is defined as: Displacement per unit time in the period throughout the motionffixix xvt t-�-Average speed is defined as: Interval Time TotalTraveled Distance TotalvCan someone tell me what the difference between speed and velocity is?xtD=DMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu4Difference between Speed and Velocity•Let’s take a simple one dimensional translation that has many steps:Let’s call this line as X-axisLet’s have a couple of motions in a total time interval of 20 sec.+10m+15m-15m-5m -10m+5mTotal Displacement:xDTotal Distance Traveled:D =Average Velocity:ffixix xvt t-�-Average Speed:Total Distance TraveledTotal Time Intervalv �xtD=D020=0( / )m s=fix x� -i ix x= -0( )m=10 15 5 15 10 5 60( )m+ + + + + =6020=3( / )m s=Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu5Example 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- += = =+Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu6Instantaneous 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 timeMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu7Position 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.Does this motion physically make sense?Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu8Velocity vs Time PlotMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu9Displacement, Velocity and Speedxxvt�D=DΔt 0limDisplacementixxxfAverage velocitytxttxxviixffAverage speedSpent Time TotalTraveled Distance TotalvInstantaneous velocityInstantaneous speedxxvt�D=DΔt 0limMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu10Accelerationxa �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 0limMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu11Acceleration vs Time PlotMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu12Example 2.4xa =)/(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-=-xvtDDMonday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu13Meanings of Acceleration•When an object is moving in a constant velocity (v=v0), there is no acceleration (a=0)–Is there any acceleration when an object is not moving?•When an object is moving faster as time goes on, (v=v(t) ), acceleration is positive (a>0)–Incorrect, since the object might be moving in negative direction initially•When an object is moving slower as time goes on, (v=v(t) ), acceleration is negative (a<0)–Incorrect, since the object might be moving in negative direction initially•In all cases, velocity is positive, unless the direction of the movement changes.–Incorrect, since the object might be moving in negative direction initially•Is there acceleration if an object moves in a constant speed but changes direction?The answer is YES!!Monday, June 7, 2004 PHYS 1441-501, Summer 2004Dr. Jaehoon Yu14One Dimensional Motion•Let’s start with the simplest case: acceleration is a constant (a=a0)•Using definitions of average acceleration and velocity, we can derive equations of motion (description of motion, velocity and
View Full Document
Unlocking...