Two particles collide, one of which was initially moving and the other initially at rest. Is it possible for both particles to be at rest after the collision?

Not possible

Explanation:

Unless there's some extra external force to keep both particles at rest after the collision, the momentum must be conserved before and after the collision.

So before the collision, 1 particle is at rest, 1 not - > total momentum is non-zero

After the collision, both particles are at rest - > total momentum is zero which is different from before.

Therefore this is not possible.