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  1. For motion on curved path, distance/displacement > 1
  2. For motion on straight path, distance/displacement = 1
  3. For falling body, distance/displacement = 1
  4. For motion on curved path, speed/velocity > 1
  5. For motion on straight path, speed/velocity = 1
  6. An acclration is said to be uniform if
    a. Average accelration = instantaneous accelration
    b. Velocity changes uniformly
  7. When velocity is constant, then velocity time graph is a horizontal straight line
  8. If accelration is constant, then velocity time graph is a straight line which rises same height for equal intervals of time
  9. If acclration is variable, then velocity time graph is curved
  10. Suppose velocity of a body starts from 0 to v in time t then average velocity will be
    Vav = 0 + v/2 = v/2
  11. Equations for linear motion with uniform accelration are following
    a. vf = vi + at
    b. S = Vav × t = (vf + vi/2) × t
    c. S = vit + 1/2 g²
    d. vf² – vi² = 2aS
    e. S = vt = v × underroot 2H/g
  12. For vertical upward motion, use negative sign with accelration in these equations. Example: A body is thrown vertically upward with velocity 80m/s. How much height it will cover in 10sec? H= vit-0.5gt² = 80×10-0.5(10)(10)² = 800-500=300m/s
  13. To find distance covered in nth sec
    S = 5(2tn – 1) Example: A body is fallen from certain height. How much distance it will cover in 4th sec? S = 5(2×4 – 1) = 35m
  14. To find distance covered in n sec
    S = 5t² Example: A body is fallen from certain height. How much distance it will cover in 4 sec? S = 5(4)² = 80m
  15. Two bodies of same masses moving with different velocities are stopped by same force. The relation between their velocities and distances in which they are stopped is
    FS = mv²/2
    S = v²
    S1/S2 = v1²/v2²
  16. Newton’s Law of motion are applicable for only low speeds as compared to speed of light
  17. For fast moving objects, relativistic mechanics developed by Albert Einstein. It is applicable for atomic particles
  18. Newton ist law is also called law of inertia.
  19. Inertia of a body is directly proportional to mass of the body
  20. The property of inertia is possessed by all bodies in nature
  21. Intertial frame of reference , a = 0 (non accelrated) .
  22. Newton’ ist law is about non accelrated frame of reference
  23. Earth is considered to be an inertial frame of reference
  24. Non inertial frame of reference, a > 0 or a < 0
  25. Newton’ 2nd law is also called law of accelration
  26. F = ma (a inversly proportional to m) (a directly proportional to F)
    Example: A body of mass 2kg is moving with 2m/s² accelration. 2kg mass is added to the body. Now its accelration will be?? m1/m2 = a2/a1 ; 2/2+2 = a2/2 ; a2 = 1m/s²
  27. A body is moving with constant acclration, the force acting on it will be constant
  28. A body is moving with zero accelration, force acting on it will be zero
  29. A body is moving with variable accelration, force acting on it will be variable
  30. Newton’ 3rd law says every action has an equal and opposite reaction
  31. Action and reaction forces never act on same body
  32. The reaction force does not cancel the action force because they act on different bodies
    What is the effect on speed of a fighter plane chasing another when it opens fire?
    Speed of chasing plane ist decreases then increases according to newton 3rd law while speed of pursued plane increases when it returns the fire
  33. Seat belts are useful in driving because these belts change the forces of motion prevent the passengers from moving forward when a moving car stops quickly
  34. A motorcycle’s safety helmet is padded so as to extend time of injury of any collision to prevent serious injury
  35. Momentum determines how easy or difficult it is to stop a moving body
  36. The idea of linear momentum was introduced by Newton
  37. P = mv Example: If % increase in velocity or mass of body is 70%, then % increase in momentum will also be 70% because there is direct relation without any square or underroot of v, m or P
  38. SI unit is Ns
  39. Momentum is not a dot or cross product of mass and velocity. It is just a product of mass and velocity
  40. The rate of change of momentum(P/t) is equal to applied force
    Example: if velocity of a moving body of mass 2kg changes from 5m/s to 10m/s in 2sec, find force? Momentum =mvf-mvi = 20-10=10Ns ; F = P/t = 10/2 = 5N
  41. Change of momentum takes place in direction of applied force
  42. Second law in terms of linear momentum, “” force applied on body is equal to rate of change of momentum”””
  43. K.E = mv²/2 = Pv/2
  44. P = 2×K.E/v
  45. K.E and momentum are equal if v=2m/s
    K.E = Pv/2 = P×2/2 = P
  46. Product of force and time is called impulse
  47. I = Ft = mv/t × t = mv
  48. SI unit of impulse is Ns
  49. Elastic collosion : total energy, k.e and linear momentum are conserved
  50. Inelastic collision : total energy and linear momentum are conserved but k.e is not conserved
  51. If two balls at same temperature collide, then momentum is conserved
  52. When two objects of equal masses collide they inter change their velocities
  53. When a ball of mass m moving with velocity v collides with exactly similar ball of mass m which is at rest, then after collision they inter change their velocities
  54. If m2 >>> m1 and v2=0 then after collision m1 bounce back with same velocity while m2 remains stationary
  55. If m1>>>m2 and v2=0 then after collision, there is no change in velocity of m1 while m2 begins to move with approximately twice of the velocity of m1
  56. F = P/t = mv/t
    Example: Suppose Gases burn in rocket at 1000kg/s. Rocket eject gases at the rate of 2000km/s. Find force? F = v×m/t = 2×106 × 106 = 2×10¹²N
  57. Suppose water flows out from pipe at 3kg/s and its velocity changes from 5m/s to zero on striking ball.
    Force = v × m/t = 5×3 = 15N
  58. Propulsion of jet aircrafts, rocket and missile type weapons depends on application of momentum principles and law of action and reaction
  59. Rocket equation is a = mv/M
    Here M is mass of rocket. When fuel is burned and ejected, mass of rocket decreases and hence accelration increases
  60. A hose pipe ejects water at speed of 0.3m/s through a hole of area 50cm-2. If water strikes a wall normally, calculate force on wall, assuming velocity of water after striking wall is zero?
    F = Area × density × velocity² = 5×10-³×10³×0.3² = 0.45N
  61. Projectile motion is 2 dimensional motion under constant accelration due to gravity
  62. a = 0 in horizontal direction
  63. F = 0 in horziontal direction
  64. v remains unchanged in horizontal direction
  65. S = Vx × t is horizontal distance
  66. a = g in vertical direction
  67. Y = vit + 1/2 gt² = (0)t + 1/2 gt² = 1/2 gt²
  68. This vertical motion is same as for a freely falling body (vi=0)
  69. Velocity along horizontal direction is Vfx = Vix = viCos theta
  70. Velocity along vertical direction is Viy = viSin theta
  71. Vfy = Viy- at = viSin theta – at
  72. Tan theta = Vfy/Vfx = viSin theta – at/vix
  73. At highest point of trajectory, velocity is minimum not zero
  74. Height of projectile = vi² Sin² theta/2g
  75. Time of flight = 2viSin theta/g
  76. Time to reach maxi. height = viSin theta/g
  77. Range of projectile = vi² Sin2 theta/g
  78. For maximum range, theta = 45°
  79. For maximum range, R = 4H
  80. R = 4H when theta = 45°
  81. For maximum height, R = 2H
  82. R = 2H when theta = 63°
  83. For Range = Height, theta = 76°
  84. For determing ratio of range to height for any given angle, R/H = 4 [cos theta/sin theta]
  85. If sum of two angles is 90°, these angles are said to be complementory angles
  86. For complementory angles, ranges are equal
    For example at 60° and 30°, ranges are equal
    At 50° and 40°, ranges are equal
  87. Horizontal range and maximum range of projectile are related as R = Rmax Sin2theta
  88. Un-powered and un-guided missile is called ballistic missile
  89. For short ranges and flat earth, trajectory is parabolic
  90. For long ranges and curved(spherical) earth, trajectory is elliptical
  91. The graph of displacement of a vertically thrown ball varrying with time is parabolic
  92. If body is moving with uniform velocity then there will be no impulse
  93. If body is moving with variable motion then there will be impulse


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