Answer: 33.6 m/s
Step-by-step explanation:
Given
The initial mass of the object is

It breaks into two fragments of 3.5 and 2.5 kg
3.5 kg part moves at 24 m/s towards left
Suppose 2.5 kg part moves with a speed of v towards the right
As the center of mass is at rest before the collision, it continues to remain at rest after the collision.

Therefore, the velocity of 2.5 kg mass is 33.6 m/s towards right.