Whenever objects are in motion (velocity > 0)
there is energy produced due to its movement. This energy is called kinetic energy,
the energy of movement. And mathematically, kinetic energy is defined as:
K = (1/2)mv2
By inspection, we also notice that kinetic energy is the total momentum or momentum
is the rate of change of kinetic energy.
K = int(0, v, mv); p = dK/dv = mv
It is widely known that energy is neither created or destroyed. Mathematically speaking,
this simply means that the initial state of energy in a system is equal to its final state.
Ei = Ef
This statement also implies that if a ball slows down, its kinetic energy has been dissipated
into some other form however never "gone".
A ball of mass m hits a smaller ball of mass m/4 at 4 km/s and comes to rest. What is the velocity of the smaller ball?