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This is a physics problem involving mechanics, specifically dynamics with pulley systems, inclines, and friction. Here is a structured breakdown of the information given:

1. **Masses and Arrangement**:
   - **\( M_1 = 10 \, \text{kg} \)**, positioned to the left of the system.
   - **\( M_2 = P \, \text{kg} \)**, on an incline with an angle indicated (presumably calculated based on given dimensions or stated directly).
   - **\( M_3 = 15 \, \text{kg} \)**, hanging on the right.

2. **Incline Dimensions**:
   - The incline has a height of **3 m** and a length of **5 m**, allowing calculation of the angle using trigonometric relations (i.e., \( \sin \theta = \frac{3}{5} \)).

3. **Additional Parameters**:
   - Gravitational acceleration \( g = 10 \, \text{m/s}^2 \).
   - Friction coefficient between \( M_2 \) and the incline, \( \mu_k = 0.1 \).
   - \( P \) is defined as the third digit of the student's ID number.

4. **Questions**:
   - **(a)** Calculates the acceleration, speed, distance traveled, and tension in the string after 2 seconds from release.
   - **(b)** After 2 seconds, when the string on the right side breaks, determines the distance each mass has traveled and the tension in the remaining string.
   - **(c)** Calculates the time and distance required for \( M_1 \) (10 kg) and \( M_2 \) (P kg) to stop temporarily after the right string breaks.
   - **(d)** Determines the distance traveled by \( M_2 \) (P kg) 4 seconds after it temporarily stops.

To solve this problem:

1. **Set Up Forces**: Identify all forces acting on each mass, including gravitational force, frictional force on \( M_2 \), and tensions in the strings.
2. **Apply Newton’s Second Law**: For each mass, establish equations based on the net forces in their respective directions.
3. **Breakdown Each Question**:
   - Use kinematics and dynamics equations for parts (a), (b), (c), and (d) as required by each scenario.

Would you like me to walk through solving each part step-by-step or provide specific diagrams as per the instructions? 

### Related Questions:
1. What is the angle of the incline based on the provided dimensions?
2. How would changing the friction coefficient affect the motion of \( M_2 \)?
3. If the mass \( M_3 \) were increased, how would it influence the system’s acceleration?
4. What would happen if the string between \( M_2 \) and \( M_3 \) were to break earlier?
5. How can we apply energy conservation principles to cross-check the answers?

### Tip:
When working with pulley problems, always identify and separate the forces on each mass, considering both gravitational and frictional effects, to avoid confusion.

Given three blocks connected by a rope through a pulley with specific masses and dimensions, calculate the acceleration, velocity, and distance traveled after 2 seconds, along with the tension in the string. Additionally, determine the outcomes when the rope breaks and how the masses move afterward.

This physics problem involves a pulley system with three masses, including one on an inclined plane. Learn how to calculate acceleration, velocity, tension in the string, and the distances traveled by the masses under various conditions. Ideal for university-level physics students.

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