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Motion in One Dimension

Motion in One Dimension. Working with Vectors. Parallel vectors have the same direction. (Ex). 2) Vectors can be moved without being changed as long as the direction and the length remain unchanged (Ex). 3) The vectors moving in opposition direction (180 ˚ turn-around) have a negative sign.

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Motion in One Dimension

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  1. Motion in One Dimension

  2. Working with Vectors • Parallel vectors have the same direction. (Ex)

  3. 2) Vectors can be moved without being changed as long as the direction and the length remain unchanged (Ex)

  4. 3) The vectors moving in opposition direction (180 ˚ turn-around) have a negative sign

  5. 4) Vectors can be added, subtracted, multiplied or divided. a) The resultant vector is the sum of vectors. b) Treat subtraction as adding “the opposite” c) Vectors can be multiplied or divided by a scalar *We don’t multiply or divide vectors here

  6. Adding Vectors • The head (tip)-to-tail method Adding Vectors Demo (Ex) Find the resultant vector.

  7. Subtracting Vectors • Change the subtraction to “adding the opposite” (Ex) Find

  8. Multiplying Vector by Scalar • Multiply the magnitude but keep the same direction (Ex) Find (Ex) Find

  9. Vectors vs. Scalar • Vector QuantitiesScalar Quantities • displacement distance • velocity speed • acceleration mass • momentum • force

  10. Symbols to Know 0 xi xf • ti= initial time • tf = final time 3) △t = time interval = duration = tf−ti 4) xi = initial position 5) xf = final position 6) △x = xf − xi= displacement = distance with direction (from the initial to final position)

  11. Displacement 0 xi xf 1) Change from initial position to final position 2) a vector quantity 3) △x = xf − xi= distance with direction (from the initial to final position)

  12. xf = 25 m xi = 11 m (Ex) Determine displacement, △x (a) 0 (b) (c) 0 xf = 25 m xi = -11m 0 xf= -11m xi=25 m

  13. Distance 1)a scalar quantity (= magnitude of displacement) 2) distance = (Ex) Determine the distance of each of previous examples.

  14. Velocity • A vector quantity of how fast an object is moving in which direction • The magnitude of velocity = speed • Average velocity • Expressed as (the boldfaced vmeans vector, “‒” above v means average) • Instantaneous velocity • Shortened as velocity • Expressed as v *Since we can’t write boldfaced, must know velocity is a vector quantity.

  15. Position-Time Graphs • 2-variable coordinate system (displacement vs. time) • Displacement on y-axis • Time on x-axis • Linear graph or curve displacement, m time, sec

  16. Possible Motions • An object stalled • An object moving forward: • at a constant speed (Ex) • while its speed is increasing at a constant rate (Ex) • while its speed is increasing but at a slower rate (Ex)

  17. An object moving backward: • at a constant speed (Ex) • while its speed is increasing at a constant rate (Ex) • while its speed is increasing but at a slower rate (Ex)

  18. Velocity • A vector quantity – has the same direction as the displacement • average velocity, • instantaneous velocity, *Know what negative velocity means (Ex)

  19. Average Velocity • Change in position divided by time interval • time interval = a scalar • displacement = a vector • Has the same direction as the displacement • Same as the slope of the line that connects that the initial and final positions • Don’t confuse with speed:

  20. Average Velocity Animation

  21. Find the average velocity. During a race on level ground, Andra covers 825 m in 137 s while running due west. Find Andra’s average velocity.

  22. *Don’t confuse: • velocity with speed (2) distance with displacement (3) average velocity vs. actual velocity (4) negative velocity (5) 0 velocity = not moving?

  23. Find the Average Velocity.

  24. Find the equation of line in terms of (1) di, d, t,and ⊽ (2) di, d, t, △d, and △t (3) d, di, df, ti, tf, and t

  25. (Examples) • What is the average velocity from 0 s to 2 s? • What is the average velocity from 1 s to 3 s? • What is the average velocity from 2 s to 4 s? • Why differ in answers though they have the same time interval? • (5) Describe the average velocity of an accelerating object.

  26. Graphs of Motions 1) Constant positive velocity How does the graph change for a higher velocity? At a lower velocity?

  27. 2) Constant negative velocity Constant Negative Velocity Animation

  28. 3)

  29. 4)

  30. 5)

  31. 6) 7)

  32. Instantaneous Velocity • Velocity at an instant • at an instant: △t = 0 or ti = tf • a vector quantity • Direction • Magnitude (Ex) An object is moving north at a constant speed of 60 mph since 6 AM today. (1) What is its instantaneous velocity at 8:15 AM? (2) What is its average velocity between 10:00 am and 11:00 AM?

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