Chek the correctness of the relation, `S_(n_(th)) = u +(a)/(2)(2n -1),` where u is initial velocity, a is acceleratin and `S_(n_(th))` is the distance travelled by the body in nth second.

Explanation

To check the correctness of the given relation \( S_{n_{th}} = u + \frac{a}{2}(2n - 1) \), we will use dimensional analysis. Dimensional analysis involves checking if both sides of the equation have the same dimensions.

### Step-by-Step Solution:

1. **Identify the dimensions of each term in the equation:**

- \( S_{n_{th}} \): Distance traveled in the \( n \)-th second.
- \( u \): Initial velocity.
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