Derive an equation for position - time (s= ut + 1/2at^2 ) relation for an object that travelled a distance 's' in time 't' under uniform acceleration 'a'.
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Explanation:
Acceleration is defined as rate of change of velocity.
hence acceleration a = (v-u)/t ..................(1)
where u and v are initial and final velocity respectively and t is time taken to change velocity from u to v.
eqn.(1) can be rewritten as, v = u+at ....................(2)
Let us asume te motion is with constant accelerated motion and its acceleration is a
Let in time t, the velocity is changed from u to v. Average velocity is (u+v)/2
distance S travelled in time t = [ (u+v)/2 ] t .......................(3)
in Eqn.(3), let us substitute for v from eqn.(2), then distance S = [ (u+u+at)/2 ] t = u t + (1/2) a t2
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