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Accelerated Motion

Accelerated Motion. Velocity, acceleration and gravity. How fast do things fall. Reflexes. Position-Time Graphs. 1. 2. 3. 4. Velocity v. Time. Velocity Change in position with respect to time v = Δ d/ Δ t Which can be written as: (d final -d initial )/(t final -t initial )

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Accelerated Motion

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  1. Accelerated Motion Velocity, acceleration and gravity

  2. How fast do things fall

  3. Reflexes

  4. Position-Time Graphs 1 2 3 4

  5. Velocity v. Time

  6. Velocity Change in position with respect to time v = Δd/Δt Which can be written as: (dfinal-dinitial)/(tfinal-tinitial) Common notation: (df–di)/(tf–ti) Acceleration Change in velocity with respect to time a = Δv/Δt Which can be written as: (vfinal-vinitial)/(tfinal-tinitial) Common notation : (vf–vi)/(tf–ti) Definitions

  7. Velocity to Acceleration • v=Δd/Δt=(dfinal–dinitial)/(tfinal–tinitial) • a=Δv/Δt=(vfinal–vinitial)/(tfinal–tinitial)

  8. Average Acceleration • a =Δv/Δt=(vfinal–vinitial)/(tfinal–tinitial) • f= final • i = initial • If tinitial = 0 • a = (vfinal – vinitial)/tfinal • Or: • vf = vi +atf

  9. Positive and Negative Acceleration

  10. Practice Problem • A soccer player is running at a constant velocity of 50.0km/h (31mph). The player falls and skids to a halt in 4.0 seconds. • What is the average acceleration of the player during the skid? • What is the plot of the velocity vs. time?

  11. Practice Problem • A water balloon in the sling of a water balloon launcher undergoes a constant acceleration 25m/s^2 for 1.5s. • What is the velocity of the water balloon right after launch?

  12. Practice Problem • A car accelerates from rest at 5 m/s2 for 5 seconds. It moves with a constant velocity for some time, and then decelerates at 5 m/s2 to come to rest. The entire journey takes 25 seconds. Plot the velocity-time graph of the motion.

  13. Practice Problem Determine the accelerations for a1, a2, a3, and a4 for each time interval. a1= 4/5 a2= (4-4)/(10-5) a3= (16-4)/(20-10) a4= (0-16)/(30-20)

  14. Gravity Hypotenuse Frictionless Cars

  15. Frictionless Car Plots

  16. Good Reading on Plot

  17. 2 ½ 2 ½ Velocity with Constant Acceleration • Given: • Solve • for tf: • Substitute in: • Yeilds:

  18. Velocity with Constant Acceleration • Solve for vf 2 ½ 2 1 1 ½ 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2

  19. Graphs • Determine which equations provide the area under the graph. (let ti = 0) (vf-vi) (tf-ti) ½ 1) Velocity (m/s) 2) 2 a tf ½ 3) (vf-vi) 2 1 (tf-ti) 2 (tf-ti) Time (s)

  20. Velocity with Constant Acceleration • Equation to remember: • vf^2 = vi^2 +2a(df-di)

  21. Position with Average Acceleration • Δd/Δt = Δv + ½ a Δt • Δd = ΔvΔt + ½ a Δt^2 • When ti = 0: • df - di = vitf + ½ atf^2

  22. Position with Average Acceleration • Equation to remember: • Final position = initial position + (change in velocity)*time + ½ (acceleration)*(time squared) • df = di + (vf-vi)t + ½ at^2

  23. Table 3-3 Page 68 • Equations of Motion for Uniform Acceleration

  24. Free Fall on the Moon

  25. Free Fall on the Moon

  26. Group Project pg 78 • How fast is the Earth spinning? • 0.5 km/sec    • How fast is the Earth revolving around the Sun? • 30 km/sec    • How fast is the Solar System moving around the Milky Way Galaxy? • 250 km/sec    • How fast is our Milky Way Galaxy moving in the Local Group of galaxies? • 370 km/sec

  27. Free Fall • All Objects fall at the same speed regardless of mass (if you can neglect wind resistance).

  28. Free Fall • A ball or a bullet? • . • . Position with Average Acceleration Height with constant gravity

  29. Falling

  30. Poor little guy

  31. Graphs

  32. Cart Movement

  33. Practice Problems • If you throw a ball straight upward, it will rise into the air and then fall back down toward the ground. • Imagine that you throw the ball with an initial velocity of 10.0 m/s. • a. How long does it take the ball to reach the top of its motion? • b. How far will the ball rise before it begins to fall? • c. What is its average velocity during this period?

  34. a. How long does it take the ball to reach the top of its motion?

  35. b. How far will the ball rise before it begins to fall?

  36. c. What is its average velocity during this period?

  37. Practice Problem • A sudden gust of wind increases the velocity of a sailboat relative to the water surface from 3.0 m/s to 5.5 m/s over a period of 60.0 s. • a. What is the average acceleration of the sailboat? • b. How far does the sailboat travel during the period of acceleration?

  38. a. What is the average acceleration of the sailboat?

  39. b. How far does the sailboat travel during the period of acceleration?

  40. Practice Problem • A car starts from rest with an acceleration of 4.82 m/s^2 at the instant when a second car moving with a velocity of 44.7 m/s (100mph by the way) passes it in a parallel line. How far does the first car move before it overtakes the second car? • Setup an equation or graph

  41. Setup the equation 0 0

  42. Positiond

  43. Velocityv=Δd/Δt

  44. Accelerationa=Δv/Δt

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