Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 1 PHYS 1441 – Section 002 Lecture #4 Wednesday, Sept. 15, 2010 Dr. 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, 2010 2 PHYS 1441-002, Fall 2010 Dr. Jaehoon YuWednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 4 Reminder: 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. 27Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 5 Displacement, Velocity and Speed One dimensional displacement is defined as: The average velocity is defined as: The average speed is defined as: Displacement per unit time in the period throughout the motion Displacement is the difference between initial and final potions of the motion and is a vector quantity. How is this different than distance? Unit? m/s Unit? m Unit? m/sWednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 6 Example 2.1 • Displacement: • Average Velocity: • Average Speed: 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?Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 7 How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m/s? Example Distance Run by a JoggerWednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 8 Andy 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 What is the speed? What is the speed?Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 9 Instantaneous Velocity and Speed • Can average quantities tell you the detailed story of the whole motion? *Magnitude of Vectors are Expressed in absolute values • Instantaneous speed is the size (magnitude) of the velocity vector: • Instantaneous velocity is defined as: – What does this mean? • Displacement in an infinitesimal time interval • Average velocity over a very short amount of time NO!!Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 10 Position vs Time Plot time t1 t2 t3 t=0 Position x=0 x1 1 2 3 1. 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, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 11Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 12 Velocity vs Time PlotWednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 13 Displacement, Velocity and Speed Displacement Average velocity Average speed Instantaneous velocity Instantaneous speedWednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 14 Acceleration analogs to analogs to Change of velocity in time (what kind of quantity is this?) • Average acceleration: • Instantaneous acceleration: Average acceleration over a very short amount of time. Vector! Unit? m/s2 Dimension? [LT-2]Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 15 Acceleration vs Time Plot What does this plot tell you? Yes, you are right!! The acceleration of this motion is a constant!!Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 16 Example 2.3 A car accelerates along a straight road from rest to 75km/h in 5.0s. What is the magnitude of its average acceleration?Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 17 Few Confusing Things on 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!!Wednesday, Sept. 15, 2010 PHYS 1441-002, Fall 2010 Dr. Jaehoon Yu 18 One Dimensional Motion • Let’s focus on the simplest case: acceleration is a constant (a=a0) • Using the definitions of average acceleration and velocity, we can derive equations of motion (description of motion, velocity and position as a function of time) (If tf=t and ti=0) For constant acceleration, average velocity is a simple numeric average
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