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# CBSE Class 9 Answered

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'
Asked by divyapragya277 | 11 Oct, 2020, 12:29: PM
Expert Answer

### 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 aLet in time t, the velocity is changed from u to v. Average velocity is (u+v)/2distance 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

Answered by Shiwani Sawant | 12 Oct, 2020, 11:26: PM

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