Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

JEE: Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

The document Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE is a part of the JEE Course Mock Test Series for JEE Main & Advanced 2022.
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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 velocityRevision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEEof a body during a time interval ?t is defined as,
    vav = average speed
    = ?s/?t
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • Instantaneous speed and velocity are defined at a particular instant and are given by
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    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  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE  over a time interval ?t.  
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    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
     Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
     
     Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
     
     Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (b) Motion with constant velocity
      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (c) Motion with constant acceleration
      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (d) Motion with constant deceleration
      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

      Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE

  • 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- Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Vector addition is associative-  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Vector addition is distributive-  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • 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.
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Magnitude of resultant vector Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    R=√(A2+B2+2ABcosθ)
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Here θ is the angle between Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE and Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    If β is the angle between Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE and  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    then,
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • 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, Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • Parallelogram law of vector addition:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    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, Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • Resolution of vector in a plane:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • Product of two vectors:-
    (a) Dot product or scalar product:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Here A is the magnitude of  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEEB is the magnitude of Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEEand θ  is the angle betweenRevision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (i) Perpendicular vector:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (ii) Collinear vector:-
    When, Parallel vector (θ = 0°), Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    When, Anti parallel vector (θ = 180°), Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (b) Cross product or Vector product:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Here A is the magnitude of Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE , B is the magnitude of Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE is the angle betweenRevision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEEand Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE and Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE is the unit vector in a direction perpendicular to the plane containing Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (i) Perpendicular vector (θ = 90°):-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    (ii) Collinear vector:-
    When, Parallel vector (θ = 0°), Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE (null vector)
    When, θ = 180°,  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE (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,
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • Area:-
    Area of triangle:-  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Area of parallelogram:-  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    Volume of parallelepiped:-  Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • 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    
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
  • (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,
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
    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:-
    Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE
The document Revision Notes: Kinematics Notes | Study Mock Test Series for JEE Main & Advanced 2022 - JEE is a part of the JEE Course Mock Test Series for JEE Main & Advanced 2022.
All you need of JEE at this link: JEE

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