I assume this question is to get the derivation, " S = u×t + (1/2)×a×t2 ", where S is the distance travel,
u is initial velocity, a is uniform acceleration and t time taken to travel the distance S.
Let us assume in a time interval t the moving object is subjected to uniform acceleration a and moving in a straight line.
Let its initial velocity is u and its final velocity is v.
average velocity = (u+v)/2 .
distance travelled = average-velocity×time, hence S = [ (u+v)/2 ]×t ...........(1)
Initial and final velocity are related as, v = u+ a×t ......................(2)
let us substitute eqn.(2) in (1), then we get S = u×t + (1/2)×a×t2