Question

Using dimension verify the corrections of a physical equation
$S=ut+\frac{1}{2}{at}^2$

Answer 1

Physical equation is correct if LHS and RHS have same dimensional formula

so , $s=ut+\frac{1}{2}a{t}^2$ have dimension

$\left[M^0{L}^1{T}^0\right]=\left[L{T}^{-1}\right]\left[T\right]+\left[L{T}^{-2}\right]$

$\left[L\right]=\left[L\right]+\left[L\right]$

since LHS and RHS have same dimension so equation is dimensionally correct