KE and MONMENTUM

Momentum

In classical mechanics, momentum is the product of the mass and velocity of an object For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. It is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector quantity, since it has a direction as well as a magnitude. Angular momentum is a pseudovector quantity because it gains an additional sign flip under an improper rotation. The total momentum of any group of objects remains the same unless outside forces act on the objects .

Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change. This law is also true in special relativity.

Kinetic Energy
The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude would be required to return the body to a state of rest from that velocity.
Kinetic energy for single objects is completely frame-dependent(relative). For example, a bullet racing by a non-moving observer haskinetic energy in the reference frame of this observer, but the samebullet has zero kinetic energy in the reference frame which moves withthe bullet. The kinetic energy of systems of objects, however, maysometimes not be completely removable by simple choice ofreference frame. When this is the case, a residual minimum kineticenergy remains in the system as seen by all observers, and this kineticenergy (if present) contributes to the system's invariant mass, which is seen as the same value in all reference frames, and by all observers.

Momentum is a vector quantity which means mass in motion.
Mathematically, momentum is given by the product of the mass of
a object and the veclocity of it.

ie. P= m*v (where P is the momentum)

In an isolated system (ie. no external force incurred), momentum is
always conserved. That means the momentum of an object is always
a constant.
Therefore, momentum is very useful in the calculation of collision
of objects.
The formula of collision (elastic):

m1*v1 + m2*v2 = m2*u1 + m2*u2
(where m1 and m2 are the masses of 2 objects, v1 and v2 are the
final velocity whereas u1 and u2 are the initial velocity)
Also, momentum is not considered as a form of energy.

As for kinetic energy, it is a vector which measures the amount of energy that causes
an object to move.
It is given by the formula:

KE = 1/2 m*v^2
Note that kinetic energy can be transferred to another types of
energy, such as potential energy.

To sum up, momentum is used to calculate collision (elastic).
Unlike kinetic energy, momentum is not considered as a form of
energy and is always conserved in an isolated system.

Mometum is defined as the product of mass of an object and its velocity. The rate of change of momentum gives the force acting on it.
Kinetic energy and momentum are two different physical quantities. They are used to describe the motion of an object under different situations. The main advantage of momentum is that it is always conserved within an isolated system, whereas kinetic energy can be transformed to other forms of energy.