2. Chapter 2: Motion in One Dimension Section 1: Displacement & Velocity

3. Mechanics Kinematics  Describes the motion of objects without looking at the cause of the motion Dynamics  Deals with the effect that forces have on motion

4. Motion  the change of an object’s position relative to some reference point

5. Describing Motion Most basic information needed: position and time Whether or not an object is in motion depends on the reference point you choose.

6. Measuring Motion Scalar quantity  Have magnitude (numerical value) but no direction Vector  Have magnitude and direction “Quantity” is the root word for quantitative… you get a number answer

7. Distance Distance (d) – how far an object travels.  Does not depend on direction. Imagine an ant crawling along a ruler. What distance did the ant travel?  d = 3 cm cm 012345678910

8. Distance Distance does not depend on direction. Here’s our intrepid ant explorer again. Now what distance did the ant travel?  d = 3 cm Does his direction change the answer? cm 012345678910

9. Distance Distance does not depend on direction. Let’s follow the ant again. What distance did the ant walk this time? d = 7 cm cm 012345678910

10. Examples of directions: + and – N, S, E, W Angles In order to define displacement, we need a direction (depends on your frame of reference)

11. Displacement vs. Distance Example of distance:  The ant walked 3 cm. Example of displacement:  The ant walked 3 cm EAST. An object’s distance traveled and its displacement aren’t always the same!

12. cm 012345678910 + - Displacement Let’s revisit our ant, and this time we’ll find his displacement. Distance: 3 cm Displacement: +3 cm  The positive gives the ant a direction!

13. Displacement Find the ant’s displacement again.  Remember, displacement has direction! Distance: 3 cm Displacement: -3 cm cm 012345678910 + -

14. Displacement Find the distance and displacement of the ant. Distance: 7 cm Displacement: +3 cm cm 012345678910 + -

15. Displacement vs. Distance An athlete runs around a track that is 100 meters long three times, then stops. – What is the athlete’s distance and displacement? Distance = 300 m Displacement = 0 m Why?

16. Displacement can be either positive or negative…depending on your frame of reference. The right (or east) will be considered positive unless otherwise stated. Likewise with up (north). The left (or west) will be considered negative unless otherwise stated. Likewise with down (south). PositiveNegative ∆ x = 8 cm ∆ x = -4 cm

18. Speed vs Velocity

19. Speed Speed (s) – Rate at which an object is moving. speed = distance / time s = d/t Like distance, speed does not depend on direction.

20. Speed A car drives 100 meters in 5 seconds. What is the car’s average speed?  s = d/t  s = (100 m) / (5 s) = 20 m/s 100 m 1 s2 s3 s4 s5 s

21. Average velocity – the total displacement divided by the total amount of time during the displacement. Velocity may be + or -, depending on the displacement. Velocity: v = ∆x = (x f -x i ) ∆t (t f – t i )

22. Why refer to it as average velocity? Example: Suppose you traveled from your house to school…a distance of 4.0 km. It took you.20 hours (12 minutes) because of heavy traffic. Your avg velocity would be: v = 4.0 km /.20 h v = 20 km/h Did you travel at that exact speed for the entire trip? Of course not. Because of this, velocity is an average.

23. Velocity and speed are not the same:  Velocity requires direction.  Speed refers to the numerical value of velocity.

24. Avg. Speed and Avg. Velocity I walk 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and average velocity. Average speed: 0.50m/s Displacement is 0 meters, average velocity is 0m/s

25. Pulling It All Together Back to our ant explorer!  Distance traveled: 7 cm  Displacement: +3 cm  Average speed: (7 cm) / (5 s) = 1.4 cm/s  Average velocity: (+3 cm) / (5 s) = +0.6 cm/s cm 012345678910 + - 1 s2 s3 s4 s5 s

26. Example

27. Using the velocity equation, we can derive another equation to find an object’s position

28. Velocity can be determined using a position vs time graph. The slope of the line corresponds to the velocity.

29. Position vs Time Object 1 Object 2 Object 3 Time Position How could we describe the motion of these objects?

30. Review Constant Velocity Positive Velocity Positive Velocity Changing Velocity (acceleration) Slow, Rightward(+) Constant Velocity Fast, Rightward(+) Constant Velocity

31. Graphing ! x t A B C A … Starts at home (origin) and goes forward slowly B … Not moving (position remains constant as time progresses) C … Turns around and goes in the other direction quickly, passing up home 1 – D Motion

32. What is the AVERAGE speed of the bass boat depicted in the graph? Average speed is taking the total distance traveled (0 to 125 meters), and dividing by the total time (1 to 9 seconds) it takes.

33. What is the instantaneous speed of the bass boat at t=7 seconds? Instantaneous Speed = 85 meters = 12.1 m/s 7 seconds

34. Example Sketch a position vs. time and a velocity vs. time graph for the following: Your mother walks five meters to the kitchen at a velocity of 2 m/s, pauses by the refrigerator for three seconds, then walks back with a plate full of potato salad at a velocity of 1 m/s.

35. At track practice, the coach makes the team members run back and forth between two lines three times

36. A car is driving down the road at 55 mph, and after getting a flat tire moves at 35 mph