Question

Equation s=ut+1/2at 2 is independent of final velocity. State how...?

Answer 1

$\mathrm{S=ut+ \frac{1}{2} at^2} \\\\ \mathrm{So,final~velocity (vt)?} \\\ \mathrm{User~a~derivative~formla:} \\\ \boxed{\mathrm{y= \frac{dx}{dt} \Rightarrow \frac{at^n}{dt} =nat^{n-1}}} \\\\ \mathrm{vt= \frac{dS}{dt}} \\\ ~~~~~\mathrm{= \frac{ut+ \frac{1}{2}at^2 }{dt} } \\\ ~~~~~\bold{\mathrm{= u+at}}$

Answer 2

s = u t + 1/ 2  a t²  is not independent of final velocity...

s = [u+at  + u] /2  * t
   = (v+u) t / 2

the above equations are same as 
          s = v t - 1/2 a t²

So equation for s  is not independent of v.