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Kinematics

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Kinematics PDF Notes, Important Questions and Synopsis

 SYNOPSIS

 

  • For motion in a straight line, the position to the right of the origin is taken as positive and that to the left of the origin is taken as negative.

  • A body in straight line motion can have the line of path as vertical, horizontal or slanted.

  • Path length is defined as the total length of the path traversed by an object.

  • Distance: Total path length covered during a given time interval.

  • Displacement: Shortest straight line distance between the initial and final position.

  • Path length is greater or equal to the magnitude of the displacement between the same points.

  • An object is said to be in uniform motion in a straight line if its displacement is equal in equal intervals of time. Otherwise, the motion is said to be non-uniform.

  • Average speed: Total distance travelled divided by the total time taken.

  • Average velocity: Total displacement divided by the total time taken.

  • The average speed of an object is greater or equal to the magnitude of the average velocity over a given time interval.

  • The slope of the x–t graph gives the velocity at a given instant.

  • The position–time graph of a body in non-uniform motion is curved.

  • The velocity–time graph of a body in non-uniform accelerated motion is curved.

  • The slope of a v–t graph gives the acceleration at that instant.

  • The area between the v–t graph and the time axis gives displacement.

  • The steepness of the slope of the position–time graph gives us the magnitude of the velocity and its sign indicates the direction of the velocity.

  • If the tangent to the position–time curve slopes upward to the right on the graph, then the velocity is positive.

  • If the tangent to the position–time graph slopes downward to the right, then the velocity is negative.

  • For one-dimensional motion, the slope of the velocity–time graph at a time gives the acceleration of the object at that time.


  • A projectile is an object on which the only force acting is gravity.

  • Projectile motion can be thought of as two separate simultaneously occurring components of motion along the vertical and horizontal directions.

  • During a projectile’s flight, its horizontal acceleration is zero and its vertical acceleration is −9.8 m/s2.

  • The trajectory of a particle in projectile motion is parabolic.

  • When a body P moves relative to a body B and B moves relative to A, the velocity of P relative to A is the velocity of P relative to B + velocity of P relative to A.
        begin mathsize 12px style straight V with rightwards arrow on top subscript straight P divided by straight A end subscript plus straight V with rightwards arrow on top subscript straight P divided by straight B end subscript plus straight V with rightwards arrow on top subscript straight B divided by straight A end subscript
straight V with rightwards arrow on top subscript straight A divided by straight B end subscript equals straight V with rightwards arrow on top subscript straight B divided by straight A end subscript end style

  • Motion of a boat in a stream

    Let velocities of boat (A) and stream (B) be begin mathsize 12px style straight V subscript straight A end styleand begin mathsize 12px style straight V subscript straight B end style , respectively, with respect to the ground.

    The velocity of boat (A) with respect to stream (B) is
    begin mathsize 12px style text V end text subscript text AB end text end subscript text =V end text subscript text A end text end subscript text -V end text subscript text B end text end subscript rightwards double arrow text V end text subscript text A end text end subscript text =V end text subscript text AB end text end subscript text +V end text subscript text B end text end subscript end style  

    Resultant velocity
     begin mathsize 12px style text V end text subscript text A end text end subscript text = end text square root of text V end text to the power of text 2 end text end exponent subscript text AB end text end subscript text +V end text to the power of text 2 end text end exponent subscript text B end text end subscript text +2V end text subscript text AB end text end subscript text V end text subscript text B end text end subscript text Cosα end text end root end style

    Time to cross the stream
    begin mathsize 12px style straight t equals straight d over straight V subscript Ay straight equals fraction numerator straight d over denominator straight V subscript AB cosθ end fraction end style 

    Shortest interval to cross the stream
    begin mathsize 12px style text t= end text straight d over straight V subscript AB end style

    Time is minimum when the denominator is maximum, so at , the time to cross the stream is minimum.

 

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