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# give me the expression for ut=1/2at square in physics

Asked by thejuraj2002 18th September 2018, 10:37 PM
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
Answered by Expert 19th September 2018, 8:52 AM
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