Question

A perfectly
collision occurs when two objects stick together and kinetic energy is lost.

Answer 1

You mean a perfectly inelastic collision. Correct sentence:
"A perfectly inelastic collision occurs when two objects stick together and kinetic energy is lost."

Key points
- Momentum is conserved (no external impulse): m1 v1 + m2 v2 = (m1 + m2) vf.
- Kinetic energy is not conserved in general; some KE is converted into internal energy (heat, deformation, sound).
- Final velocity (1D): vf = (m1 v1 + m2 v2) / (m1 + m2).

Kinetic energy lost
Let initial KE = 1/2 m1 v1^2 + 1/2 m2 v2^2 and final KE = 1/2 (m1 + m2) vf^2. The loss equals
ΔK = K_initial − K_final = 1/2 · (m1 m2)/(m1 + m2) · (v1 − v2)^2,
which is always ≥ 0 and zero only when v1 = v2 (no relative motion).

If you want, I can show a numeric example or a short derivation.