Check the correctness of following equation by the method of dimensions :
`S=ut+(1)/(2)at^(2)` .
where S is the distance covered bu a body in time t, having initial velocity u and acceleration a.

Explanation

To check the correctness of the equation \( S = ut + \frac{1}{2}at^2 \) using the method of dimensions, we will analyze the dimensions of each term in the equation.

### Step-by-Step Solution:

1. **Identify the terms in the equation**:
The equation is \( S = ut + \frac{1}{2}at^2 \).
Here, \( S \) is the distance covered, \( u \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.

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