We can write (at^2)/2+ut as (at^2+2ut)/2, if you mean so the question has been answered.
This represents the distance S covered an object with an initial velocity u and a uniform accelaration a in time t i.e. S=(at^2)/2+ut or S=(at^2+2ut)/2.
It may be noted that if initial velocity is u and uniform accelaration is a, then the velocity after t units of time v is given by
v=u+at and average velocity barv is given by barv=(v+u)/2 i.e.
but as S=(at^2+2ut)/2=(t(at+u+u))/2=(t(v+u))/2
or we can say S=barvxxt, where barv is average velocity.
Note that the different formulas are used in different circumstances and though (at^2)/2+ut simplifies to barvxxt, these are used depending on what variables are given to us, regarding motion with uniform accelaration. One more important formula is v^2-u^2=2aS.
