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I: Intro to Kinematics: Motion in One Dimension

I: Intro to Kinematics: Motion in One Dimension. AP Physics C Mrs. Coyle . Particle Model Position Vector Displacement, distance Average Velocity, Average Speed Instantaneous Velocity, Instantaneous Speed Intro to the Derivative. Graphical Analysis (position vs time)

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I: Intro to Kinematics: Motion in One Dimension

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  1. I: Intro to Kinematics: Motion in One Dimension AP Physics C Mrs. Coyle

  2. Particle Model • Position Vector • Displacement, distance • Average Velocity, Average Speed • Instantaneous Velocity, Instantaneous Speed • Intro to the Derivative. • Graphical Analysis (position vs time) • Uniform Linear Motion

  3. Video Clip of Oil Spill in Gulf • http://www.youtube.com/watch?v=_2EXDmnNPw0

  4. Motion • Motion is relative • Origin • Position is compared to an origin • Coordinate system or a reference frame

  5. Motion Diagram t=0.50 sec t=0.75 sec t=0.25 sec t=0 sec

  6. Particle Model . . . . . t=0.50s t=0 t=0.25s t=0.75s

  7. Position Vectors y=+4 m o x= 5m x= 10 m x= -5m Position (m)

  8. Position Vectors o x=10m x=20m Position (m)

  9. Vectors and Scalars • Scalars  Magnitude (size) • Vectors  Magnitude and Direction

  10. Displacement (Dx): change in position.Dx =xf - xi Dx o x1=15m x2=20m Position, x (m)

  11. Distance and Displacement • Distance: (Scalar) • Displacement Dx =xf - xi(Vector)

  12. Average Speed and Average Velocity • Average Speed= Total Distance Travelled Time (Scalar) • Average Velocity= Displacement =Dx Time Dt (Vector)

  13. Prob. #2.4 • A particle moves according to the equation x=10t2 (x in meters, t in seconds). • Find the average velocity for the time interval from 2s to 3s. • Ans: 50m/s

  14. Instantaneous SpeedInstantaneous Velocity • Instantaneous Speed • Speed at a given instant. (Time is very very small) • Instantaneous Velocity • Velocity at a given instant. (Time is very very small) • Instantaneous speed is the magnitude of instantaneous velocity.

  15. Instantaneous Velocity: the limit of Dxas Dt approaches 0.Dt v = limDx Dt0Dt v = dx dt

  16. Instantaneous Velocity (or simply) Velocity is the derivative of x with respect to t. v = dx dt

  17. Instantaneous Velocity • Instantaneous speed is the magnitude of instantaneous velocity.

  18. Graphical Analysis of Motion • Position vs Time • Velocity vs Time • Acceleration vs Time

  19. Example 1: Graph of Position vs Time Position (m/s) o Time (s) • Slope of Line= Average Velocity • In this case does the slope also equal the instantaneous velocity?

  20. Uniform Linear Motion • Motion with constant velocity • Straight line • Same direction

  21. Example 2: Graph of Position vs Time Position (m) o Time (s) Instantaneous Velocity at a given time= Slope of Tangent at that time

  22. Example 2: Graph of Position vs Time Position (m) 40.0 20.0 o 2.0 Time (s) Find the instantaneous velocity at 2sec and the average velocity from 0 to 2sec.

  23. Example 3: Position vs Time Graph Position, (m) • At what time(s) was the object at the origin? • What is the average velocity from 0 to 1sec, 1 to 1.5 sec and 0 to 2sec? 20.0 10.0 A o 0.5 1.0 1.5 2.0 -10.0 Time, (s)

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