Derive three equation of motion by graphical metod

1.	Derive three equation of motion by graphical metod
Answer» We have the third equation of motion as,v2 = U2 + 2aSWhere,v is the final velocity,S is said to be as displacement of the particle,u is the initial velocity,a = acceleration (constant),At t = 0 sec, u is the initial velocity of the particle.At t = t sec, v is the final velocity of the particle.Now, if we draw the graph for the above set of statements then, from the graph we have,(Displacement)S = Area of Rectangle + Area of Triangle{tex}S=\\frac{u t+1}{2(v-u)(t)}{/tex}\xa0.........eqn1From the first equation of motion we have\xa0{tex}t=\\frac {(v-u)}{a}{/tex}Now let us substitute the value of t in eqn 1{tex}S=u\\left(\\frac{v-u}{a}\\right)+\\frac{\\frac{1}{2}((v-u)(v-u))}{a}{/tex}By simplifying and rearranging the terms,We get the expression asv2 = u2 + 2aS = third equation of motion.Hence the third equation of motion is proved with the help of graphical method.\xa0

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