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Prove the second equation of motion graphically and define the slope of the graph |
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Answer» Proof of the second equation of motion graphically is as follows,Let us consider a BODY which is moving with the initial velocity vi.Then the final velocity of the body is vf with the time t in sec.The distance traveled =S, then the acceleration of the body is indicated as a.That is, Initial velocity =viFinal velocity = vfTime TAKEN =tAcceleration=aDistance=SSo now, let us consider the speed of the body by OA which as initial velocity as vi and OC the speed of the body OC at final velocity vfThen the slope of the graph AB will REPRESENT acceleration of the body with a.S=area of OABCS= area of rectangle OADC+ area of triangle ABDThen S=(vi)(t)+1/2(AD)(BD)By substitution we GET the above expression to be as,\bold{S=(v i)(t)+1 / 2 a t^{2}}S=(vi)(t)+1/2at 2 |
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