Given information:
- Two particles of mass m collide with each other.
- One particle is at rest before the collision.
- The velocity of the other particle before the collision is given as 3i - 2j m/s.

Analysis:
- Since the collision is elastic, both momentum and kinetic energy are conserved.
- Momentum: The total momentum before the collision is equal to the total momentum after the collision.
- Kinetic Energy: The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Solution:

Momentum conservation:
- Let the particle at rest have a velocity of 0 m/s.
- The total momentum before the collision is given by the sum of the individual momenta of the particles.
- Total momentum before collision = Momentum of particle 1 + Momentum of particle 2
- Momentum of particle 1 = m * (3i - 2j)
- Momentum of particle 2 = m * (0)
- Total momentum before collision = m * (3i - 2j) + m * (0)
- Total momentum before collision = m * (3i - 2j)

- After the collision, the particles move in opposite directions.
- Let the velocity of the other particle after the collision be V.
- The total momentum after the collision is given by the sum of the individual momenta of the particles.
- Total momentum after collision = Momentum of particle 1 + Momentum of particle 2
- Momentum of particle 1 = m * (3i - 2j)
- Momentum of particle 2 = m * V
- Total momentum after collision = m * (3i - 2j) + m * V
- Total momentum after collision = m * (3i - 2j) + m * V

- According to the principle of momentum conservation, the total momentum before the collision is equal to the total momentum after the collision.
- Therefore, m * (3i - 2j) = m * (3i - 2j) + m * V

Kinetic energy conservation:
- The total kinetic energy before the collision is given by the sum of the individual kinetic energies of the particles.
- Total kinetic energy before collision = Kinetic energy of particle 1 + Kinetic energy of particle 2
- Kinetic energy of particle 1 = (1/2) * m * ((3i - 2j) dot (3i - 2j))
- Kinetic energy of particle 2 = (1/2) * m * (V dot V)
- Total kinetic energy before collision = (1/2) * m * ((3i - 2j) dot (3i - 2j)) + (1/2) * m * (V dot V)

- After the collision, both particles continue to move with different velocities.
- The total kinetic energy after the collision is given by the sum of the individual kinetic energies of the particles.
- Total kinetic energy after collision = Kinetic energy of particle 1 + Kinetic energy of particle 2
- Kinetic energy of particle 1 = (1/2) * m * ((3i - 2j) dot (3i - 2j))
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