Final answer:
The velocities of the pieces after an explosion will be radially outward from the point of explosion, and the center of mass of the system will continue with the same velocity it had before the explosion in the absence of external forces.
Step-by-step explanation:
In an explosion of an object, such as a 34 kg object breaking into three parts, the pieces will move according to the conservation of momentum. The velocities of the exploding pieces will be radially outward from the point of explosion. This is because, at the instant of the explosion, all the internal forces cancel out, and hence the explosion has radial symmetry. Centripetal acceleration is present only when an object is moving along a circular path and is directed toward the center of the circle. In the case of an explosion, there is no centripetal force acting on the pieces after they have separated, thus the concept of centripetal acceleration does not apply post-explosion.
The center of mass of the system (the object prior to explosion) will continue to move in the same direction with the same velocity it had before the explosion if no external forces are acting on the system. If air resistance is significant, it will slow down the motion of the center of mass after the explosion.