1. Chapter 2 Motion in One Dimension 2-1 Velocity and Displacement

2. Kinematics  Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.  We will learn to describe motion in two ways. »Using graphs »Using equations

3. Particle  A particle is an object that has mass but no volume and occupies a position described by one point in space.  Physicists love to turn all objects into particles, because it makes the math a lot easier.

4. Position  How do we represent a point in space?  a) One dimension  b) Two dimensions  c) Three dimensions (x) (x,y) (x,y,z)

5. Distance (d)  The total length of the path traveled by a particle.  “How far have you walked?” is a typical distance question.  SI unit: meter (m)

6. Displacement (  x)  The change in position of a particle.  “How far are you from home?” is a typical displacement question.  Calculated by…  x = x final – x initial  SI unit: meter (m)

7. Delta (  )   is a Greek letter used to represent the words “change in”.  x therefore means “change in x”. It is always calculated by final value minus initial value.

8. A B 50 m displacement 100 m distance Distance vs Displacement  A picture can help you distinquish between distance and displacement.

9. Practice Problem A particle moves from x = 1.0 meter to x = -1.0 meter. a) What is the distance d traveled by the particle? b) What is the displacement of the particle? 2.0 m -2.0 m

10. Practice Problem Question: If  x is the displacement of a particle, and d is the distance the particle traveled during that displacement, which of the following is always a true statement? a) d = |  x| b) d < |  x| c) d > |  x| d) d > |  x| e) d < |  x|

11. Practice Problem You get on a ferris wheel of radius 20 meters at the bottom. When you reach the top on the first rotation a) what distance have you traveled? b) what is your displacement from the bottom? c) When you are on your way back down, does the distance increase, decrease, or stay the same? What about the displacement? d) What is the distance traveled after you have completed the full ride of 10 rotations? What about the displacement?

12. Practice Problem answers You get on a ferris wheel of radius 20 meters at the bottom. When you reach the top on the first rotation a) d = ½ (2  r) =  r = 20  m b)  x = 20 + 20 = 40 m c) distance increases, displacement decreases d) d = 10 (2  r) = 400  m

13. Average Speed  How fast a particle is moving.  s ave = d  t where: s ave = rate (speed) d = distance  t = elapsed time  SI unit: m/s Average speed is always a positive number.

14. Average Velocity  How fast the displacement of a particle is changing.  v ave = ∆x ∆t where: v ave = average velocity ∆x = displacement ∆t = change in time  SI unit: m/s Average velocity is + or – depending on direction.

15. Practice Problem A car makes a trip of 1½ laps around a circular track of diameter 100 meters in ½ minute. For this trip a) what is the average speed of the car? b) what is its average velocity? 15.7 m/s 3.33 m/s

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17. Practice Problem How long will it take the sound of the starting gun to reach the ears of the sprinters if the starter is stationed at the finish line for a 100 m race? Assume that sound has a speed of about 340 m/s. Answer: 0.29 s

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19. Practice Problem Describe the motion of this particle. It is stationary. t x

20. Practice Problem Describe the motion of this particle. It is moving at constant velocity in the + x direction. t x

21. Graph: Position vs Time What physical feature of the graph gives the constant velocity? The slope, because  x/  t is rise over run! t x xx tt A B v ave =  x/  t

22. Practice Problem Determine the average velocity from the graph. Ans: 1/3 m/s x (m)

23. Graph: Position vs Time Does this graph represent motion at constant velocity? No, since there is not one constant slope for this graph. t x

24. Graph: Position vs Time Can you determine average velocity from the time at point A to the time at point B from this graph? Yes. Draw a line connecting A and B and determine the slope of this line. t x A B xx tt v ave =  x/  t

25. Practice Problem Determine the average velocity between 1 and 4 seconds. Ans: 0.17 m/s

26. Instantaneous Velocity  The velocity at a single instant in time.  Determined by the slope of a tangent line to the curve at a single point on a position-time graph.

27. Instantaneous Velocity Draw a tangent line to the curve at B. The slope of this line gives the instantaneous velocity at that specific time. t x B xx tt v ins =  x/  t

28. Practice Problem Determine the instantaneous velocity at 1.0 second. Ans: 0.8 m/s