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Graphical Derivation of First EquationConsider 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 = atv = u + at  I equation of motionGraphical Derivation of Second EquationDistance travelled S = area of the trapezium ABDO= area of rectangle ACDO + area of DABC(v = u + at I eqn of motion; v - u = at)Graphical Derivation of Third EquationS = 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  III Equation of Motion
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