V=vi+at^2 dimensional correct

Yes, dimensionally the equation is correct.

Explanation:

This equation is the kinematic equation for uniformly accelerated motion, then we study the units of each member to conclude whether it is dimensionally correct.

vi = initial velocity [m/s]

a = acceleration [m/s^2]

t = time [s]

v = final velocity

therefore we have:

[m/s] + [m/s^2]*[t^2], the second term now is m/s

[m/s] + [m/s] = [m/s]

So the analysis is correct.