**Understanding the Problem:**

To effectively solve advanced level numerical problems in motion in one dimension, it is essential to first understand the problem statement. Break down the problem into smaller components and identify the given information and what is being asked.

**Procedure:**

1. **Read the problem carefully:** Make sure to understand all the given information, variables, and conditions mentioned in the problem.

2. **Identify the knowns and unknowns:** Differentiate between the given parameters and the ones you need to find.

3. **Choose an appropriate equation:** Based on the given information and the unknowns, select the relevant equation(s) from the equations of motion.

4. **Solve for the unknown:** Substitute the known values into the equation(s) and solve for the unknown variable.

5. **Check the solution:** Verify the obtained answer by analyzing whether it is reasonable and satisfies the conditions mentioned in the problem.

**Example Problem:**

Let's consider an example to understand the process better:

*Problem: A car starts from rest and accelerates uniformly at 2 m/s² for 10 seconds. Calculate the final velocity and the distance traveled by the car during this time.*

**Given:**
- Initial velocity (u) = 0 m/s
- Acceleration (a) = 2 m/s²
- Time (t) = 10 s

**Unknowns:**
- Final velocity (v)
- Distance traveled (s)

**Solving the Problem:**

1. **Read the problem carefully:** The problem states that a car starts from rest (u = 0) and accelerates uniformly at 2 m/s² for 10 seconds.

2. **Identify the knowns and unknowns:**
- Knowns: u = 0 m/s, a = 2 m/s², t = 10 s
- Unknowns: v (final velocity), s (distance traveled)

3. **Choose an appropriate equation:**
We can use the equation: v = u + at to find the final velocity and the equation: s = ut + (1/2)at² to find the distance traveled.

4. **Solve for the unknown:**
- Using v = u + at: v = 0 + (2 m/s²)(10 s) = 20 m/s
- Using s = ut + (1/2)at²: s = (0 m/s)(10 s) + (1/2)(2 m/s²)(10 s)² = 100 m

5. **Check the solution:**
The obtained values are reasonable, as the car starts from rest and accelerates at a constant rate, resulting in a final velocity of 20 m/s. The distance traveled during this time is 100 meters.

By following these steps and understanding the problem thoroughly, one can effectively solve advanced level numerical problems in motion in one dimension.