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 | 11th 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 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 

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