Kinematics, JEE Main Notes JEE Notes | EduRev

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  • Inertial frame of reference:- Reference frame in which Newtonian mechanics holds are called inertial reference frames or inertial frames. Reference frame in which Newtonian mechanics does not hold are called non-inertial reference frames or non-inertial frames.
  • The average speed vav and average velocityKinematics, JEE Main Notes JEE Notes | EduRevof a body during a time interval ?t is defined as,
    vav = average speed
    = ?s/?t
    Kinematics, JEE Main Notes JEE Notes | EduRev
  • Instantaneous speed and velocity are defined at a particular instant and are given by
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Note:
    (a) A change in either speed or direction of motion results in a change in velocity
    (b) A particle which completes one revolution, along a circular path, with uniform speed is said to possess zero velocity and non-zero speed.
    (c) It is not possible for a particle to possess zero speed with a non-zero velocity.
  • Average acceleration is defined as the change in velocity  Kinematics, JEE Main Notes JEE Notes | EduRev  over a time interval ?t.  
    Kinematics, JEE Main Notes JEE Notes | EduRev
    The instantaneous acceleration of a particle is the rate at which its velocity is changing at that instant.
  • The three equations of motion for an object with constant acceleration are given below.
    (a) v = u+at
    (b) s = ut+1/2 at2
    (c) v2 = u2+2as
    Here u is the initial velocity, v is the final velocity, a is the acceleration, s is the displacement travelled by the body and t is the time.
    Note: Take ‘+ve’ sign for a when the body accelerates and takes ‘–ve’ sign when the body decelerates.
  • The displacement by the body in nth second is given by,
    sn = u + a/2 (2n-1)
  • Position-time (x vs t), velocity-time (v vs t) and acceleration-time (a vs t) graph for motion in one-dimension:
    (i) Variation of displacement (x), velocity (v) and acceleration (a) with respect to time for different types of motion.  
     
    Displacement(x)
    Velocity(v)
    Acceleration (a)
    (a) At rest
     Kinematics, JEE Main Notes JEE Notes | EduRev
     
     Kinematics, JEE Main Notes JEE Notes | EduRev
     
     Kinematics, JEE Main Notes JEE Notes | EduRev
    (b) Motion with constant velocity
      Kinematics, JEE Main Notes JEE Notes | EduRev

      Kinematics, JEE Main Notes JEE Notes | EduRev

      Kinematics, JEE Main Notes JEE Notes | EduRev
    (c) Motion with constant acceleration
      Kinematics, JEE Main Notes JEE Notes | EduRev
      Kinematics, JEE Main Notes JEE Notes | EduRev

      Kinematics, JEE Main Notes JEE Notes | EduRev
    (d) Motion with constant deceleration
      Kinematics, JEE Main Notes JEE Notes | EduRev

      Kinematics, JEE Main Notes JEE Notes | EduRev

    Kinematics, JEE Main Notes JEE Notes | EduRev

  • Scalar Quantities:- Scalar quantities are those quantities which require only magnitude for their complete specification.(e.g-mass, length, volume, density)
  • Vector Quantities:- Vector quantities are those quantities which require magnitude as well as direction for their complete specification. (e.g-displacement, velocity, acceleration, force)
  • Null Vector (Zero Vectors):- It is a vector having zero magnitude and an arbitrary direction.
    When a null vector is added or subtracted from a given vector the resultant vector is same as the given vector.
    Dot product of a null vector with any arbitrary is always zero. Cross product of a null vector with any other vector is also a null vector.
  • Collinear vector:- Vectors having a common line of action are called collinear vector. There are two types.
    Parallel vector (θ=0°):- Two vectors acting along same direction are called parallel vectors.
    Anti parallel vector (θ=180°):-Two vectors which are directed in opposite directions are called anti-parallel vectors.
  • Co-planar vectors- Vectors situated in one plane, irrespective of their directions, are known as co-planar vectors.
  • Vector addition:-
    Vector addition is commutative- Kinematics, JEE Main Notes JEE Notes | EduRev
    Vector addition is associative-  Kinematics, JEE Main Notes JEE Notes | EduRev
    Vector addition is distributive-  Kinematics, JEE Main Notes JEE Notes | EduRev
  • Triangles Law of Vector addition:- If two vectors are represented by two sides of a triangle, taken in the same order, then their resultant in represented by the third side of the triangle taken in opposite order.
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Magnitude of resultant vector Kinematics, JEE Main Notes JEE Notes | EduRev
    R=√(A2+B2+2ABcosθ)
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Here θ is the angle between Kinematics, JEE Main Notes JEE Notes | EduRev and Kinematics, JEE Main Notes JEE Notes | EduRev
    If β is the angle between Kinematics, JEE Main Notes JEE Notes | EduRev and  Kinematics, JEE Main Notes JEE Notes | EduRev
    then,
    Kinematics, JEE Main Notes JEE Notes | EduRev
  • If three vectors acting simultaneously on a particle can be represented by the three sides of a triangle taken in the same order, then the particle will remain in equilibrium.
    So, Kinematics, JEE Main Notes JEE Notes | EduRev
  • Parallelogram law of vector addition:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Cases 1:- When, θ = 0°, then,
    R = A+B (maximum), β = 0°
    Cases 2:- When, θ = 180°, then,
    R= A-B (minimum), β = 0°
    Cases 3:- When, θ = 90°, then,
    R = √(A2+B2), β = tan-1 (B/A)
  • The process of subtracting one vector from another is equivalent to adding, vectorially, the negative of the vector to be subtracted.
    So, Kinematics, JEE Main Notes JEE Notes | EduRev
  • Resolution of vector in a plane:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
  • Product of two vectors:-
    (a) Dot product or scalar product:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Here A is the magnitude of  Kinematics, JEE Main Notes JEE Notes | EduRevB is the magnitude of Kinematics, JEE Main Notes JEE Notes | EduRevand θ  is the angle betweenKinematics, JEE Main Notes JEE Notes | EduRev
    (i) Perpendicular vector:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
    (ii) Collinear vector:-
    When, Parallel vector (θ = 0°), Kinematics, JEE Main Notes JEE Notes | EduRev
    When, Anti parallel vector (θ = 180°), Kinematics, JEE Main Notes JEE Notes | EduRev
    (b) Cross product or Vector product:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Here A is the magnitude of Kinematics, JEE Main Notes JEE Notes | EduRev , B is the magnitude of Kinematics, JEE Main Notes JEE Notes | EduRev is the angle betweenKinematics, JEE Main Notes JEE Notes | EduRevand Kinematics, JEE Main Notes JEE Notes | EduRev and Kinematics, JEE Main Notes JEE Notes | EduRev is the unit vector in a direction perpendicular to the plane containing Kinematics, JEE Main Notes JEE Notes | EduRev
    (i) Perpendicular vector (θ = 90°):-
    Kinematics, JEE Main Notes JEE Notes | EduRev
    (ii) Collinear vector:-
    When, Parallel vector (θ = 0°), Kinematics, JEE Main Notes JEE Notes | EduRev (null vector)
    When, θ = 180°,  Kinematics, JEE Main Notes JEE Notes | EduRev (null vector)
  • Unit Vector:- Unit vector of any vector is a vector having a unit magnitude, drawn in the direction of the given vector.
    In three dimension,
    Kinematics, JEE Main Notes JEE Notes | EduRev
  • Area:-
    Area of triangle:-  Kinematics, JEE Main Notes JEE Notes | EduRev
    Area of parallelogram:-  Kinematics, JEE Main Notes JEE Notes | EduRev
    Volume of parallelepiped:-  Kinematics, JEE Main Notes JEE Notes | EduRev
  • Equation of Motion in an Inclined Plane:
    (i) Perpendicular vector :-  At the top of the inclined plane (t = 0, u = 0 and a = g sinq ), the equation of motion will be,
    (a) v= (g sinθ)t                                                          
    (b) s = ½ (g sinθ) t2
    (c) v2 = 2(g sinθ)s    
    Kinematics, JEE Main Notes JEE Notes | EduRev
  • (ii) If time taken by the body to reach the bottom is t, then   s = ½ (g sinθ) t2
    t = √(2s/g sinθ)
    But sinθ =h/s   or s= h/sinθ
    So, t =(1/sinθ) √(2h/g)
    (iii) The velocity of the body at the bottom
    v = g(sinθ)t
    =√2gh
  • The relative velocity of object A with respect to object B is given by
    VAB = VA-VB
    Here, VB is called reference object velocity.
  • Variation of mass:- In accordance to Einstein’s mass-variation formula, the relativistic mass of body is defined as,
    m= m0/√(1-v2/c2)
    Here, m0 is the rest mass of the body, v is the speed of the body and c is the speed of light.
  • Projectile motion in a plane:- If a particle having initial speed u is projected at an angle θ (angle of projection) with x-axis, then,
    Kinematics, JEE Main Notes JEE Notes | EduRev
    Time of Flight, T = (2u sinα)/g
    Horizontal Range, R = u2sin2α/g
    Maximum Height, H = u2sin2α/2g
    Equation of trajectory, y = xtanα-(gx2/2u2cos2α)
  • Motion of a ball:-
    (a) When dropped:-  Time period, t = √(2h/g) and speed, v = √(2gh
    (b) When thrown up:- Time period, t = u/g and height, h = u2/2g
  • Condition of equilibrium:-
    Kinematics, JEE Main Notes JEE Notes | EduRev
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