In a perfectly inelastic collision, the two objects stick together after the collision, forming a single mass. To find the common velocity of the two objects after the collision, you can use the principle of conservation of linear momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

The formula for linear momentum is:

Momentum (p) = mass (m) × velocity (v)

Before the collision:

For the first object (2 kg, 5 m/s): Momentum = (2 kg) × (5 m/s) = 10 kg*m/s

For the second object (3 kg, at rest): Momentum = (3 kg) × (0 m/s) = 0 kg*m/s

The total momentum before the collision is 10 kg*m/s.

After the collision, the two objects stick together, forming a single mass of 2 kg + 3 kg = 5 kg. Let the common velocity after the collision be v (m/s). Now we can set up the equation using the conservation of momentum:

Total momentum after the collision = 5 kg × v

Since momentum is conserved:

10 kg*m/s = 5 kg × v

Now, solve for v:

v = (10 kg*m/s) / (5 kg) = 2 m/s

So, the common velocity of the two objects after the perfectly inelastic collision is 2 m/s.