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Introduction to Kinematics: Motion in One Dimension - AP Physics

Explore motion in one dimension with concepts like position vectors, displacement, average velocity, and more. Learn about the particle model, derivatives, and graphical analysis of motion. Engage with examples and a video clip on uniform linear motion.

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Introduction to Kinematics: Motion in One Dimension - AP Physics

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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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