Given information:
- Mass of M1 = 4 kg
- Mass of M2 = kg (unknown)
- Time = 9 seconds

Task:
- Find the distance traveled by the center of mass in 9 seconds.
- Calculate the speed of the center of mass after 9 seconds.

Solution:
To solve this problem, we need to use the concept of conservation of momentum and the equations of motion.

Step 1: Find the mass of M2:
Since the mass of M1 is given as 4 kg, we need to find the mass of M2. Let's assume it to be M2 kg. Therefore, the total mass (M) of the system is the sum of the masses of M1 and M2:

M = M1 + M2
M = 4 kg + M2 kg

Step 2: Find the initial velocity of the center of mass:
Since both masses are initially at rest, the initial velocity of the center of mass (Vcm) is zero.

Step 3: Find the distance traveled by the center of mass:
To find the distance traveled by the center of mass, we can use the equation of motion:

Distance = Initial velocity * Time + (0.5 * Acceleration * Time^2)

Since the initial velocity of the center of mass is zero, the equation simplifies to:

Distance = 0.5 * Acceleration * Time^2

The acceleration of the center of mass can be calculated using the equation:

Acceleration = Total force / Total mass

Since only the force of gravity acts on the system, the total force is the weight of the system, given by:

Total force = Total mass * Gravity

Substituting the values:

Total force = (4 kg + M2 kg) * 9.8 m/s^2

Now we can substitute the value of acceleration into the distance equation:

Distance = 0.5 * [(4 kg + M2 kg) * 9.8 m/s^2] * (9 s)^2

Step 4: Find the speed of the center of mass after 9 seconds:
The final speed of the center of mass can be calculated using the equation of motion:

Final velocity = Initial velocity + (Acceleration * Time)

Since the initial velocity is zero, the equation simplifies to:

Final velocity = (Acceleration * Time)

Substituting the values:

Final velocity = [(4 kg + M2 kg) * 9.8 m/s^2] * 9 s

Summary:
- The distance traveled by the center of mass in 9 seconds is given by the equation: Distance = 0.5 * [(4 kg + M2 kg) * 9.8 m/s^2] * (9 s)^2
- The speed of the center of mass after 9 seconds is given by the equation: Final velocity = [(4 kg + M2 kg) * 9.8 m/s^2] * 9 s