We know that during fragmentation (explosion) of any material the particles possess equal Kinetic motion which is given by the formula
KE= \frac{1}{2} mv².
In the first particle , m=2 kg ,v= 3 m/s
⇒KE= \frac{1}{2} * 2 * 3² J
= \frac{1}{2} *2 * 9 J
= 9 J
In the second particle let the required velocity be v.
The kinetic energy of both particles need to be equal.
 \frac{1}{2} *1*v² =9
or, v=√18
Ans:The velocity of the piece of 1 kg is √18 m/s.
3 3 3