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Displacement

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  1. Position Distance Displacement Chapter 2-1

  2. Position Position of an object is measured as a distance from a stationary reference point.

  3. Frame of Reference Examples: • The position of a moving car is relative to a tree.

  4. Frame of Reference • The Sun is the “Frame of Reference” for the planets.

  5. Displacement The length of the straight line drawn from a moving object’s initial position to its final position is called.

  6. Language of Physics Delta means “Change In”

  7. ΔX = Xf– Xi ΔX=change in position Xf = final position Xi= initial position

  8. Distance vs. Displacement Distance is how far an object moves over an entire trip. finish start Displacement is a straight-line path between an objects starting point and finish point. finish start

  9. Distance vs. Displacement DISTANCE = 10 mi + 7 mi = 17 mi 7 mi 10 mi Final position initial position 13 mi DISPLACEMENT = 13 mi

  10. Describing Motion with Words A physics teacher walks 4 meters East. Then he turns and walks 2 meters directly South, turns again to walk 4 m directly West, then finally heads 2 m North returning to his starting position. 2 m 2 m 4 m 4 m

  11. Describing Motion with Words • During the course of the teacher's motion, he has walked a distance of __12_meters. • However, since he has returned to his starting point, his displacement is __0__ meters.

  12. Sign of Displacement Positive- upward y(+) x Negative-to the left Positive-to the right (+) (-) (-) (+) (+) (-) Negative- downward

  13. diagram below

  14. 390 m 390 mm 130 m.

  15. A soccer player changes position back and forth on the field. In the diagram below each position is marked where the player reverses direction. The player moves from position A to B to C to D. • Find the distance and displacement of travel.

  16. Describing Motion with Words Solution Distance = 85 m Displacement = 55 m

  17. Scalars • A quantity that has only magnitude (a number value) Does not give direction object moves • Examples: speed v = 2.4 m/s distance x = 4 m

  18. Vectors • A quantity with both magnitude and direction • Examples: velocity (v= 2.4 m/s to the NORTH) displacement (x = 4 m left)

  19. Speed vs Velocity: different meaning - same equation Speed (scalar) • speed = distance/time v = x/t • scalar quantity-has only magnitude Velocity(vector) • velocity= displacement/time v = x/t • Vector quantity- has both magnitude and direction

  20. Vectors Represented with Arrows Displacements are represented by vector arrows. Each vector is drawn proportionate to its magnitude, and pointing in a direction. V= 50 m/s east V= 100 m/s east

  21. Velocity HOW FAST AN OBJECT IS MOVING

  22. v = x / t Average velocity = displacement / time • Units: meters/second (m/s) • Can be positive or negative depending on direction moved. • Average velocity, constant velocity, and speed are all the same equation. • Time can never be negative!

  23. Average Velocity

  24. Constant Velocity • The velocity does not change. Ex: A car with its cruise control on maintains a constant speed.

  25. Instantaneous speed is speed at a particular moment in time. • horse race photo finish • represented as a single point on a graph

  26. If you graph position on the y-axis and time on the x-axis, the slope of the line is equal to the average velocity. • Slope = rise = position = velocity run time

  27. Slope of the line in a Position/Time Graph is Velocity velocity position time Slope = rise = position = velocity run time

  28. 25 20 15 10 5 Constant Positive Velocity Zero Velocity POSITION (m) Constant Negative Velocity 0 5 10 15 20 25 TIME (sec)

  29. Acceleration

  30. Acceleration • A change in velocity per unit time • It is a vector quantity and must have a direction • SI units for Acceleration m/s2

  31. Equation Acceleration

  32. Acceleration • Acceleration is the measure of how fast something speeds up, slows down or turns.

  33. Velocity and Acceleration

  34. Acceleration

  35. Accelerating Versus Decelerating • A negative acceleration doesn’t always mean the object is slowing down. It could be moving in the negative direction.

  36. Constant Acceleration • Example: Velocity and displacement increase by the same amount each time interval

  37. Instantaneous Acceleration • Acceleration at an instant in time

  38. Average Acceleration a = vf – vi t Change in velocity divided by time taken to make this change

  39. Slope of a graph describes the objects motion

  40. 4 Kinematic Equations • All the kinematic equations are related. • There is always more than one way to solve each problem. • In general though, one equation is generally easier to use then others.

  41. Equations - Kinematic • Vf = vi +at • ∆x=vi(t) + ½ a(t)2 • ∆x = ½ (Vi +Vf)∆t • Vf2 = Vi2 +2ax

  42. Practice 2C • #1. A car accelerates from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels. • Knowns? • vi = 0m/s, vf = 23.7km/h (6.58 m/s), t = 6.5 s • Unknowns? • Distance = ?, x= ? • Equation? • ∆x = ½ (Vi +Vf)∆t • Answer = ? • x = .5 (6.58)(6.5) =21.38 m

  43. Practice Heather and Matthew walk eastward with a speed of .98 m/s. If it takes them 34 min to walk to the store, how far have they walked? • Given: Speed = .98 m/s, time = 34 minutes (2040 sec) • Unknown: How far? Distance = ? • Equation: Speed = distance / time v = d/t • rearrange for distance d = vt • Substitute/Solve: d = (.98 m/s) (2040 s) d = 1999.2 meters