You give a crate a push to set it in motion. After the push is over, the crate skids to a stop on a rough, level floor. Describe the energy changes after the push (with the crate as the system).

KE₁ = PE₂

Explanation:

From the principle of conservation of energy we know that

KE₁ + PE₁ = KE₂ + PE₂

where KE is the kinetic energy and PE is potential energy  

KE = ½mv²

PE = mgd

Initially, you gave a push to crate and it started moving with some velocity

KE₁ = ½mv₁²

Initially, the potential energy is zero since it didnt cover any distance

PE₁ = mgd₁ = 0

At the final state, the crate stopped and its finally velocity become zero, therefore, the kinetic energy is zero.

KE₂ = ½mv₂² = 0

At the final state, the crate covered some distance and the final potential energy is

PE₂ = mgd₂

Therefore, the energy relation becomes

KE₁ + PE₁ = KE₂ + PE₂

KE₁ + 0 = 0 + PE₂

KE₁ = PE₂

Hence, the initial kinetic energy of the system is converted to final potential energy of the system.

b) phosphorus pentoxide