Question

establish the relation s= ut + 1/2 at, where symbols have their usual meaning

Answer 1

Distance travelled = Avg velocity * time
S=(u+v)/2*t
[But v=u+at]
S={u+(u+at)}/2*t
S={(2u+at)/2}*t
S=ut+1/2at^2

Answer 2

Consider an object which has travelled displacement s in the time t under uniform acceleration a.Let intial velocity of the object be u and the final velocity v.

s=1/2t(u+v) -1

from the veocity relation

v=u+at -2

substitute 1 in 2

s=1/2t(u+u+at)

=1/2t(2u+at)

s=ut+1/2at^2

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