A bullet is shot into a metal plate and comes to a stop. It experiences an impulse I. An identical bullet travelling at the same speed is shot into thick layers of cloth and comes to a stop. How does the second bullets impulse compare to the first?

the second bullet and the first bullet will both have equal amount of impulse m(V - u) = m(0 - u) = -mu

Explanation: impulse is the change of momentum or the products of force and time.

Ft = m(v-u) = impulse.

Both bullets posses equal amount of force, both bullets will experience equal impulse in coming to rest since they posses equal mass and their initial and final velocities are u and V respectively.

V = 0 sinice they both come to rest.

Ft = m(0 - u) = -mu,

The -ve sign indicates it is towards the direction opposite the direction of motion.

The bullet that penetrates the plate will come to rest faster compared to the bullet that penetrates the layer of clothes.

This means the bullet that penetrates the cloth spends a longer time before coming to rest and hence meets a lesser resistant force compared to the bullet that penetrates the block.