The correct equation of motion is :

Explanation

To determine the correct equation of motion, we need to analyze the three primary equations that describe motion in one dimension. These equations are derived from the definitions of velocity, acceleration, and displacement.

### Step-by-Step Solution:

1. **Identify the Equations of Motion**:
The three main equations of motion are:
- First Equation: \( v = u + at \)
- Second Equation: \( s = ut + \frac{1}{2} a t^2 \)
- Third Equation: \( v^2 = u^2 + 2as \)

2. **Evaluate Each Option**:
We will evaluate the given options one by one to see which one matches the standard equations of motion.

- **Option 1**: \( v = ut + a \)
- This is incorrect because the correct form is \( v = u + at \).

- **Option 2**: \( s = ut + \frac{1}{2} a t \)
- This is incorrect because the correct form is \( s = ut + \frac{1}{2} a t^2 \). The term \( t^2 \) is missing.

- **Option 3**: \( v = u + at \)
- This is correct. It matches the first equation of motion.

- **Option 4**: \( v = u + as \)
- This is incorrect as there is no such equation in the equations of motion.

3. **Conclusion**:
After evaluating all options, the only correct equation of motion is from **Option 3**: \( v = u + at \).

### Final Answer:
The correct equation of motion is **Option 3: \( v = u + at \)**.

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