How much kinetic energy is added to the system during the explosion, as measured in the observer's reference ?

Question

An object, with mass m and speed v relative to an observer, explodes into two pieces, one two times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic is added to the system during the explosion, as measured in the observer's reference frame?

Answer 1

All KE and momentum P are relative to the observer
KEinit = mv^2/2
Pinit = mv
Body 1 is the finally stationary piece of mass = m/3.
V1final = 0
P1final = 0
KE1 = 0
From conservation of momentum,
P2final = Pinit - P1final = mv
V2final = P2final/(2m/3) = 1.5v
KE2 = m(1.5v)^2/2 = 2.25*mv^2/2
KE change = KE1 + KE2 - KEinit = 1.25mv^2/2

Answer 2

@kirchway But ,what is meant by the adding of Kinetic Energy here?