(a) By the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Since the particles come to rest after the collision, the total momentum after the collision is 0.

Initial momentum: \(3.2v + 2.4(-6) = 0\)

Solving for \(v\):

\(3.2v - 14.4 = 0\)

\(3.2v = 14.4\)

\(v = \frac{14.4}{3.2} = 4.5\)

(b) The initial kinetic energy of the system is the sum of the kinetic energies of both particles:

\(KE_{initial} = \frac{1}{2} \times 3.2 \times (4.5)^2 + \frac{1}{2} \times 2.4 \times 6^2\)

\(= \frac{1}{2} \times 3.2 \times 20.25 + \frac{1}{2} \times 2.4 \times 36\)

\(= 32.4 + 43.2 = 75.6\)

The final kinetic energy is 0 since both particles come to rest.

Thus, the loss of kinetic energy is 75.6 J.