1. Representing Motion Chapter 2

2. Some Definitions and Assumptions about Motion  Particle model : focus on a single point on an extended object; the size of the object must be less than the distance it moves.  Use a coordinate system to describe an object’s position, i.e., the separation between where the object is and the origin of the coordinate system. We can locate the origin in a convenient place.  In describing motion we’ll use two different quantities.  Scalars have a single attribute, a magnitude.  Examples: distance, speed, time, temperature  Vectors have two attributes, a magnitude and a direction.  Examples: displacement, velocity, acceleration, force

3. Scalars and Vectors

4. Representing Vectors in One Dimension 01234-2-3-4 AB x

5. Combining Vectors in One Dimension 01234-2-3-4 A Vector A has a magnitude of 3 units and is in the +x direction Vector B has a magnitude of 2 units and is in the +x direction If C = A + B, the resultant vector C has a magnitude of 5 units and is in the +x direction. If D = A – B, the resultant vector D has a magnitude of 1 unit and is in the +x direction (because A – B = A + (- B ) and the vector – B has the same magnitude as B and points in the opposite direction). We can also multiply vectors by scalars. The vector E = n A is a vector whose magnitude is n times the magnitude of A and points in the same direction as A. So if n=3 then the magnitude of E is 9 units and it is in the +x direction. x 5 B C D

6. Exercises with Vectors in 1-D  Suppose we’re given three vectors A is 5 units in magnitude and points in the +x direction B is 3 units in magnitude and points in the –x direction C is 2 units in magnitude and points in the +x direction  Describe (magnitude and direction) the following resultant vectors W, X, Y and Z where 1. W = A – B 2. X = A + B + C 3. Y = B + n A ; where n=4 4. Z = A /5

7. Displacement and Time Intervals

8. Difference between Distance and Displacement video

9. Velocity and Speed

10. Equation of Motion for Object Moving with Average Velocity

11. Plotting Position vs. Time Rise = 35 Run = 17.5 Position Time y-intercept

12. 2009 World Championships in Berlin Usain Bolt 2009 World Record

13. Usain Bolt’s 100m World Record Distance (m)Time (s)Split (s)10m Average Velocity (m/s) Reaction Time0.146 101.851.7045.87 202.891.049.62 303.780.8911.24 404.640.8611.63 505.490.8511.76 606.310.8212.20 707.110.8012.50 807.920.8112.35 908.740.8212.20 1009.580.8411.90

14. Bolt’s Position vs. Time Graph

15. How Fast are Humans?

16. How Fast is 0.01 Second? Usain Bolt’s time: 9.79s; Justin Gatlin’s time: 9.80s Estimate how far apart in distance they were at the finish. Usain Bolt 2015 World Championship

17. Problem D100m At the 2015 NJ Outdoor State Championships Charlie Volker from Rumson-Fair Haven HS won the Group 2 100m dash race with a time of 10.97 seconds. How long of a lead (D) could Usain Bolt give him and finish the race in the same time? UB CV

18. Activities Super Ultimate Graphing Challenge Boat Motion Lab

19. New Horizons Mission to Pluto