Which one of the following is the equation for Position - Time relation?
A) `S= "ut" +1//2 "at"^2`
B) V = u + at
C) U = y + at
D) `2as = v^2 – u^2`

Options

A. `S= "ut" +1//2 "at"^2`
B. V = u + at
C. U = y + at
D. `2as = v^2 – u^2`

Answer

To solve the question regarding which equation represents the Position-Time relation, we need to analyze each option provided:

1. **Understanding the equations of motion**:
- There are three primary equations of motion that describe the relationship between position, velocity, acceleration, and time. These are:
1. \( V = u + at \) (Equation 1)
2. \( S = ut + \frac{1}{2}at^2 \) (Equation 2)
3. \( v^2 - u^2 = 2as \) (Equation 3)

2. **Identifying the Position-Time relation**:
- The Position-Time relation describes how the position (S) of an object changes over time (t) under constant acceleration (a).
- Among the three equations listed, the equation that directly relates position (S) to time (t) is:
\[ S = ut + \frac{1}{2}at^2 \]
- This equation shows that the position (S) is a function of the initial velocity (u), time (t), and acceleration (a).

3. **Evaluating the options**:
- **Option A**: \( S = ut + \frac{1}{2}at^2 \) - This is the correct Position-Time relation.
- **Option B**: \( V = u + at \) - This relates velocity to time, not position.
- **Option C**: \( U = y + at \) - This does not represent a standard equation of motion.
- **Option D**: \( 2as = v^2 - u^2 \) - This relates acceleration and velocity, not position directly.

4. **Conclusion**:
- The correct answer is **Option A**: \( S = ut + \frac{1}{2}at^2 \).

### Summary of Steps:
1. Identify the three equations of motion.
2. Determine which equation relates position to time.
3. Evaluate each option against the identified equation.
4. Conclude with the correct answer.