using graphical equation derive the following kinetic equation x-x0=ut+1/2at^2
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Perhaps a graphical method is best, it avoids integration which can be a stumbling block to some students who have not covered the topic yet. We start with considering the graph of v vs t. This is a straight line, starting at u, the initial velocity. The final value of the velocity is v, say, where v=u+aT. The area of the trapezium formed is 1/2 (u+v)T. That is, 1/2(u+u+aT)T. This is equal to 1/2(2uT+aT^2) which reduces to uT+1/2aT^2, as required.
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