Check whether the relation `S = ut + (1)/(2) at^(2)` is dimensionally correct or not , where symbols have their usual meaning .

Explanation

To check whether the relation \( S = ut + \frac{1}{2} at^2 \) is dimensionally correct, we will analyze the dimensions of both sides of the equation step by step.

### Step 1: Identify the dimensions of \( S \)
- The left-hand side (LHS) of the equation is \( S \), which represents distance or displacement.
- The dimension of distance (or displacement) is given by:
\[ [S] = [L] = M^0 L^1 T^0 \]
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