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Acceleration

Acceleration. Do Now: Jot down in your notes. What is the definition of acceleration? What is the first equation of acceleration. Looking at the equation, what would be the units of acceleration/. Acceleration. Any object not traveling at constant velocity is accelerating.

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Acceleration

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  1. Acceleration

  2. Do Now: Jot down in your notes • What is the definition of acceleration? • What is the first equation of acceleration. • Looking at the equation, what would be the units of acceleration/

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

  4. Velocity vs. Acceleration Velocity - rate of position change. Acceleration - rate of velocity change. Constant/Uniform accl. – change v at constant rate. To calculate average/ uniform / constant accl a = Dvvf – viDtDt

  5. Uniform / Constant Acceleration Changing speed or direction at constant rate.

  6. Units become: m Dv s = m or d/t2. Dt s s2 What does it mean to have a constant or uniform acceleration of = 10 m/s2.

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

  8. 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:

  9. a = vf –vi t a = Dv +20 m/s - 0 m/s = +10 m/s2Dt 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.

  10. 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.

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

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

  13. 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 = ?

  14. 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

  15. 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.

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

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

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

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

  20. 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)

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

  22. 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?

  23. Hwk Wksht Mixed Accl Equations • and • Review Bk pg 70 #3-13, 25 – 31 On separate sheet write out all sentences, equations, show calc’s with units.

  24. Velocity Time GraphsSpeed Time Graphs

  25. Constant Velocity/Speed

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

  27. What’s going on here?

  28. Sign of velocity is direction.

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

  30. Displacement on V-T graphs

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

  32. 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

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

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

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

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

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

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

  39. 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.

  40. Objects Falling Under Gravity

  41. Freefall Gravity accelerates masses as they fall and rise.

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

  43. But with air resistance

  44. 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.

  45. Apparent WeightlessnessObjects in Free-fall Feel Weightless

  46. What is the graph of a ball dropped?

  47. What do the d-t, v-t, and a – t, graphs of a ball thrown into the air look like if it is caught at the same height?

  48. A ball is thrown upward from the ground level returns to same height. a is 0, the ball is accelerating at constant 9.81 m/s2. velocity is + when the ball is moving upward d = ball’s height above the ground Why is acceleration negative? Is there ever deceleration?

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