Momentum vs Energy
Momentum and energy (kinetic energy) are important properties of a moving object and governed by Newton’s Laws of motion. They are both related to each other as the product of mass and velocity of a moving object is its momentum and half of the product of mass and the square of its velocity is called its kinetic energy. So when you increase the velocity of an object, you are effectively increasing its momentum, and also its kinetic energy as can be seen by the formula. But, and this is important, momentum and kinetic energy of a body are not equivalent and interchangeable.
Momentum of a moving body, according to second law of motion of Newton is the product of its mass and velocity. The law states that the rate of change of momentum is directly proportional to the force applied and it is in the direction of the force.
P = m X v = mv
Now, kinetic energy of a moving body is given as half of the product of its mass and square of its velocity
K.E = ½ m X v^{² }= ½ mv²
It is clear that both momentum and energy of a moving body are dependent upon its velocity. You double the velocity and you double the momentum of the body. But doubling the velocity quadruples the kinetic energy of the moving body.
Let us see the difference between momentum and kinetic energy through an experiment.
Given an evil chance, which of the following two would you stand in front of, a 1000kg truck moving at 1m/sec, or a meatball weighing 1 kg moving at a speed of 1000m/sec. If you are a student of physics, you would gleefully stand in front of the truck as it would at best throw you sideways without causing too much of a harm whereas the meatball moving at such a ferocious speed may even kill you. Let us see how.
P (truck) = 1000X1= 1000kg m/s
K.E (truck) = ½ X10000 X 1X 1 = 500 joules
On the other hand,
P (meatball) = 1 X 1000 = 1000 kg m/s
K.E (meatball) = ½ X 1 X 1000 X 1000 = 500000 Joules
It is thus clear that because of very high kinetic energy of the meatball, it is dangerous to stand in front of it.
In brief: Momentum vs Energy • Though momentum and kinetic energy of a moving object are related, they are not the same of equivalent. • While momentum is a vector quantity requiring direction as well, kinetic energy is a scalar quantity needing only amount. • If you double the velocity of a moving object, its momentum is doubled but the kinetic energy gets quadrupled.

Related Links:
1. Difference Between Impulse and Force
2. Difference Between Momentum and Impulse
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