Question

When a stationary bomb explode, then from where does its fragments get kinetic energy?

Answer 1

Momentum = mass x velocity (not speed).

This means that Momentum is associated with direction. So if two objects (same mass) are traveling in the opposite direction at the same speed, the total system momentum will be zero. But if moving in the same direction, then the total system momentum will be double of each object's momentum.

So - the sum total of momentum of all individual objects (flying in all possible directions) would be zero.  

Even for a bomb bursting on the ground (objects fly only upwards or sideways), the momentum is conserved (downward movement of earth).