Question

show that the expression vf = vi + at is dimensionally correct

Answer 1

I assume V is speed, which is [m/s]. So dimensions of Vf and Vi are now clear. The next term in the equation is at, which is acceleration * time. Dimensions are [m/s^2]*[s]. The dimension of at is therefore [m/s]. This means that the equation only contains elements with dimension [m/s], which is therefore dimensionally correct.