What manner of persons ought ye to be?
Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness, looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat? 2 Peter 3:11-12
How does the dissolution of this current physical world motivate the Christian to holiness? For the assumption behind the question of these two verses is that it ought to do so. The seeing of the coming dissolution and the looking for and hasting unto the coming of the day of God is the reason behind the oughtness of the holy and godly conduct pointed to.
The reason this is so is because giving into sin is always accompanied by a this-world-only perspective. We sin at least partly because we lose a proper perspective. Sin offers immediate gratification. It offers us pleasure and holds out a promise of present satisfaction. And if we hear its siren song, we will give in.
The way to stop our ears from being convinced by its deception is by reorienting our focus on the world to come and to remember that the pleasure which sin gives is (1) only temporary at best, and (2) is always followed by God's judgment (see ver. 7). On the other hand, those whom God's long-suffering has led to repentance (ver. 9), and who have made a definite break with this world, will by his grace in Christ experience everlasting joy and happiness and peace in a world in which righteousness dwells (ver. 10).
Thus, the apostle John reminds us, "Love not the world, neither the things that are in the world. If any man love the world, the love of the Father is not in him. For all that is in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world. And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever" (1 John 2:15-17).