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if s1 s2 and s3 are the distances covered by a body moving with uniform acceleration in consecutive consecutive consecutive equal interval s
Let vo be the velocity at some instant of time and a be the uniform acceleration.

if S1 is the distance travelled for time interval t , then we have,  S1 = vo t + (1/2)a t2 ............. (1)

For subsequent equal interval t after travelling distancs S1, Distance travelled S2 is given by,

S2 = ( vo + a t ) + (1/2)a t2  ............................(2)

For subsequent equal interval t after travelling distancs S2, Distance travelled S3 is given by,

S3 = ( vo + 2a t ) + (1/2)a t2  ............................(3)

from eqn.(1) and eqn.(3), we get ,  S1 + S3 = 2( vo + at ) + at2  =  2 [ ( vo + a t ) + (1/2) a t2 ] = 2 S2

hence we get ,  S2 = [ S1 + S3 ] / 2
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