Representing Motion Chapter 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

Scalars and Vectors

Representing Vectors in One Dimension AB x

Combining Vectors in One Dimension 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

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

Displacement and Time Intervals

Difference between Distance and Displacement video

Velocity and Speed

Equation of Motion for Object Moving with Average Velocity

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

2009 World Championships in Berlin Usain Bolt 2009 World Record

Usain Bolt’s 100m World Record Distance (m)Time (s)Split (s)10m Average Velocity (m/s) Reaction Time

Bolt’s Position vs. Time Graph

How Fast are Humans?

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

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 seconds. How long of a lead (D) could Usain Bolt give him and finish the race in the same time? UB CV

Activities Super Ultimate Graphing Challenge Boat Motion Lab

New Horizons Mission to Pluto