With the usual notations , check if the following equation `S_(t) = u + (1)/(2) a ( 2t -1)` is dimensionally correct or not.

Explanation

To check if the equation \( S_t = u + \frac{1}{2} a (2t - 1) \) is dimensionally correct, we will analyze the dimensions of each term in the equation.

### Step 1: Identify the dimensions of each variable

1. **Displacement \( S_t \)**: The dimension of displacement is denoted as \( [S_t] = L \) (length).
2. **Initial velocity \( u \)**: The dimension of velocity is given by \( [u] = LT^{-1} \) (length per time).
3. **Acceleration \( a \)**: The dimension of acceleration is given by \( [a] = LT^{-2} \) (length per time squared).
4. **Time \( t \)**: The dimension of time is denoted as \( [t] = T \).
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