Check the correctness of the formula `S = ut + 1/3 "at"^2` where S is the distance , u is velocity , a is acceleration and t is time.

Explanation

To check the correctness of the formula \( S = ut + \frac{1}{3} at^2 \), we will analyze the components of the equation and compare it with the standard equations of motion.

### Step 1: Understand the components of the formula
- \( S \) represents the distance traveled.
- \( u \) is the initial velocity.
- \( a \) is the acceleration.
- \( t \) is the time.

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