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    Home >> Physics >> Motion III

    Motion III

    Velocity/Time graph

    Uniform Motion- The Velocity /Time graph of an object moving in uniform motion is a straight line which passes through the origin.

    Slope = y2-y1/x2-x1                  Where y is taken from the distance and y2-y1

                                               Where x is taken from the time and x2-x

    Zero Acceleration- The graph of an object with zero acceleration is a straight line which is parallel to the x axis

    Uniform Retardation- The graph of an object with uniform retardation is a straight line and the line meets the x axis when the object comes to rest.

    Variable Retardation/Acceleration- The graph of an object with Variable Retardation/Acceleration is a curve line. The slope cannot be calculated.

    Graphical Derivations of Equations of Motion


    Graphical Derivation of First Equation

    Consider an object moving with a uniform velocity u in a straight line. Let it be given a uniform acceleration a at time t = 0 when its initial velocity is u. As a result of the acceleration, its velocity increases to v (final velocity) in time t and S is the distance covered by the object in time t.

    The figure shows the velocity-time graph of the motion of the object.

    Slope of the v - t graph gives the acceleration of the moving object.

    Thus, acceleration = slope = AB =

    v - u = at

    v = u + at 1st  equation of motion 

    Graphical Derivation of Second Equation

    Distance travelled S = area of the trapezium ABDO

    = area of rectangle ACDO + area of DABC

    (v = u + at I equation of motion; v - u = at)

           2nd Equation of motion

    Graphical Derivation of Third Equation

    S = area of the trapezium OABD.

    Substituting the value of t in equation (1) we get,

    2aS = (v + u) (v - u)

    (v + u)(v - u) = 2aS [using the identity a2 - b2 = (a+b) (a-b)]

    v2 - u2 = 2aS   3rd Equation of Motion 

    Circular Motion/Accelerated Motion

    When an object moves along a circular path with constant speed its direction keeps on changing continuously hence it is known as acceleration motion. At any instant the direction of motion is along the tangent to the circle at that point.

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