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Acceleration

This text explains the concepts of acceleration and velocity, including constant acceleration, acceleration of gravity, and velocity-time graphs. It also provides equations and examples to calculate average and uniform acceleration and displacement.

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Acceleration

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  1. Acceleration

  2. Velocity vs. Acceleration Velocity (v) - rate of position change. Constant v – rate stays the same, equal distance for equal t interval. Acceleration (a)- rate of velocity change. Constant/Uniform accl. – change v for equal time interval. To calculate average/ uniform / constant accl a = Dv a = vf – vi t t

  3. Acceleration • Any object not traveling at constant velocity is accelerating. • Changing speed – either speeding up or slowing down. • Changing direction.

  4. We will look at Uniform / Constant Acceleration Changing speed or direction at constant rate. What are units?

  5. Since a = Dv /tUnits become: m Dv s = m or d/t2. t s s2 What does it mean to have a constant or uniform acceleration of = 10 m/s2.

  6. Acceleration of Gravity (g) near the surface of the Earth. • ~ 10 m/s2. • Drop a ball from rest (vi = 0) • After 1 sec, it’s velocity ~ 10 m/s • After 2 sec, it’s velocity ~

  7. a. If I drop a ball from rest near Earth’s surface, approximately how fast is it moving after falling 5 seconds? • 50 m/s

  8. Acceleration is a vector.Magnitude & direction.When Dv is positive accl is positivesince Dv tWhat does the sign of accl mean?

  9. Sign of acceleration Sign tells change in v. 1. Consider a car starts from rest, heads east, and attains a velocity of +20 m/s in 2 s. Calculate a:

  10. a = vf –vi t a = Dv +20 m/s - 0 m/s = +10 m/s2t 2 s Acceleration is positive. The car is headed in a positive direction and speeding up. 2. Now consider the same car slowing to a stop from +20 m/s in 2s. Calculate a.

  11. Now vf is 0, and vi is +20m/s, so.a = Dv 0 m/s - (+20 m/s) = -10 m/s2. Dt 2s Accl is neg. the car is slowing down. Hold on - its not so simple! 3. Consider the same car starts from rest, heads west, and reaches 20 m/s in 2 s. Calculate a now. Since the car is heading west, the vf is neg.

  12. A quick calculation shows this new accl to be negative. Oy!Here are the rules:

  13. Velocity motion a pos speeding +pos slowing -neg speeding -neg slowing + Mental Trick!

  14. 4. A shuttle bus slows to a stop with an acceleration of -1.8 m/s2. How long does it take to slow from 9.0 m/s to rest? • List the variables. • a = -1.8 m/s2. • vi = 9 m/s • vf = 0 (stop) • t = ?

  15. a = -1.8 m/s2. • vi = 9 m/s • vf = 0 (stop) • t = ? • Find an equation with everything on the list. • a = vf– vi/t • Rearrange to solve for the unknown. • t = vf– vi/a • Plug in with units. • = 9m/s – 0 = 5 s. -1.8 m/s2

  16. 5. A plane starts from rest and accelerates for 6 minutes at 20 m/s2 before traveling at a constant velocity. What was its final velocity? • 7200 m/s.

  17. Another useful acceleration equation. • d = vit + ½ at2. • d= displacement (m) • vi = initial (starting velocity) m/s. • a = acceleration m/s2. • t = time over which accl takes place - s.

  18. 6. A car starts from rest and accelerates at 5 m/s2 for 8 seconds. How far did it go in that time? • List! • Equation! • Solve. • 160 m

  19. Acceleration Hwk. • Hwk Intro to Acceleration Rd 48 – 49 Do pg 49 #1 - 5.

  20. 1. Take your seat. • 2. Take out your physics supplies. • 3. Will 6 volunteers come to the front please

  21. Do Now: • Ruler Drop.

  22. More Acceleration Equations • a = Dv/t • vf = vi + at • d = vit + ½ at2. • vf2 = vi2 + 2 ad.

  23. 1. A car starts from rest and accelerates at 6 m/s2 for 5 seconds. How far did it travel?

  24. 2. A car slows to a stop from 23 m/s by applying the brakes over 12 meters. Calculate acceleration. • vi = 23 m/s • vf = 0 • d = 23 m • a = ? • vf2 = vi2 + 2ad • - vi2 = a • 2d • -(23 m/s)2= -22 m/s2. 2(12m)

  25. 3.A bicycle is traveling at 5 m/s. It accelerates at 3 m/s2 for 3 meters. What is its final velocity?

  26. 4. A truck skidded to a stop with an acceleration of -3 m/s2. If its initial velocity was 11 m/s, how far was it skidding before it came to a stop?

  27. Hwk Wksht Mixed Accl Equations sheet.

  28. Velocity Time GraphsSpeed Time Graphs

  29. Constant Velocity/Speed

  30. Constant / Uniform Acceleration. On velocity time graph accl. is slope of straight line.

  31. What’s going on here?

  32. Sign of velocity is direction.

  33. Sketch Graphs V-t sketch graphs Rev BookHwk Rev Book. Rd 55 – 58. Do pg 56 #7-13 AND Pg 58 #14 – 18.

  34. Displacement on V-T graphs

  35. Displacement = Area Under Curvev = d/t then, vt = d.

  36. Area of non-constant velocity. For constant accl, d = area of a triangle: ½ bh.If a car achieved a v=40 m/s in 10 s, then:½(10s)(40m/s) = 200 m. 40 m/s 10 s

  37. To find displacement, calc area of triangle + rectangle.

  38. How can you tell when object is back to starting point? • Positive displacement = negative displacement.

  39. Do Now: Given the v – t graph below, sketch the acceleration – t graph for the same motion.

  40. Acceleration – time Graphs • What is the physical behavior of the object? • Slowing down pos direction, constant vel neg accel.

  41. d-t: • slope = velocity • area ≠ . • v-t: • slope = accl • area = displ • a-t: • slope ≠ . • area = D vel • vf – vi.

  42. Hwk Rev Book pg 76 #32-36, 45-47, 49 – 55, 59-60. Begin in class.

  43. Together: text pg 65 #1-5,pg 72 # 34, 35, 48, 49. Test Thursday: Acceleration, Motion Graphs, Free-fall. Text 2-2, 2-3. RB Chap 3.

  44. Objects Falling Under Gravity

  45. Freefall Gravity accelerates uniformly masses as they fall and rise. Earth’s acceleration rate is 9.81 m/s2 – very close to 10 m/s2.

  46. Falling objects accelerate at the same rate in absence of air resistance

  47. But with air resistance

  48. Fortunately there is a “terminal fall velocity.” After a while, the diver falls with constant velocity due to air resistance. Unfortunately terminal fall velocity is too large to live through the drop.

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