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Terminology : a = acceleration, v = final velocity , u = intial velocity, t = time.
From the definition of Acceleration ,
a = v - u / t.
Now, Transposing t to Left hand side.
at = v - u
Transpose -u to Left hand side.
at + u = v.
Interchanging the sides of the equation,
v = u + at.
Now, We have two velocities " u " & " v " .
Average velocity = u + v /2 .
We know that,
Velocity = Distance / Time
Distance = Velocity * Time
s = ( u + v) t / 2
Substitute v = u + at.
s = ( u + u + at ) t /2
s = ( 2u + at) t /2
s = ut + 1/2 at² .
Hence proved !
Hope It Helped :-)
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