 # Relation Between Kinetic Energy And Momentum

### What is Kinetic Energy and Momentum?

Kinetic energy is the energy that any object or body possesses when it moves from one place to another. It is known as the energy that is necessary to accelerate an object from its state of rest to the stated velocity.

For moving a body from its constant state, one needs to apply a force to do work. Once this work gets done, the energy gets transferred to the mass that now moves at a new speed. The energy that an object receives to change its position is known as kinetic energy, and it depends on mass and velocity.

Therefore, kinetic energy can get transferred from one object to another. Also, it can change into other forms of energy.

Since all objects have a mass; if a body is in a state of movement, then it contains momentum. It depends on two variables – velocity and mass of an object.

There is a relation between kinetic energy and momentum as both the properties are linked with velocity. Momentum gets expressed as a multiplication of velocity and mass, whereas kinetic energy is the product of the square of speed and half of the mass.

### What is the Formula of Momentum and Kinetic Energy?

Since kinetic energy is directly proportional to half of the mass of an object and its velocity, it can be expressed as the following.

KE = $\frac{1}{2}$∗m∗v2

Where m = mass of a body

V = velocity of an object due to change in its motion.

If the mass contains 1 kilogram and the velocity of a body is meters/second, the kinetic energy will be 1 kg per meter square and seconds square. The standard unit (S.I.) of kinetic energy gets measured in Joules.

Where 1 Joule = 1kg m2/s2

One can calculate momentum as mass multiplied with velocity. It is expressed in the following form.

P = m∗v

Where m = mass of a substance

V = velocity

Since, both the momentum and kinetic energy depend on velocity and mass, a change in one affects the other.

### Kinetic Energy and Momentum Relationship

Kinetic energy is the energy that any substance has when it accelerates, whereas momentum is an object’s mass in motion. There is a kinetic energy and momentum relation due to their connection with mass and velocity.

The relation between kinetic energy and momentum can be mathematically shown as:

KE = $\frac{1}{2}$∗m∗v2 and momentum (p) = m∗v

Consider, KE = ½ ∗m∗v∗v

KE = (m∗v)∗($\frac{1}{2}$∗v)

KE = p∗($\frac{1}{2}$∗v)

Therefore, we can say that a body’s kinetic energy is equal to the product of momentum and half its velocity. It is the relation between linear momentum and kinetic energy of a substance.

Multiple-choice questions

Find some solved questions and answers on energy and momentum.

1. Momentum can change due to

1. Acceleration

2. Impulse

3. Force

4. All of these

1. A boxer quickly changes his move bending his head backwards when someone tries to hit him on the head. What does this motion achieve?

1. Momentum increases, force decreases

2. Contact time increases as a result force decreases

3. Contact time decrease, increasing force

4. It helps to confuse the opponent

1. An object placed in a resting posting has

1. Velocity

2. Potential energy

3. Kinetic energy

4. Momentum

1. The total energy in an object including rest energy in the world

1. Cannot change

2. Can decrease but not increase

3. May either decrease or increase

4. Can increase but not decrease

Though the study of energy and momentum is vast, we hope from the above discussion; you can understand the relation between kinetic energy and linear momentum. To access study material on related topics and concepts, install our Vedantu app and avail the online interactive sessions.

1. Does Momentum Increase with an Increase in Kinetic Energy?

Ans. Since there is a relation between KE and momentum, KE increases with a rise in momentum. For instance, a 5% increase in momentum will result in a 10% increase in kinetic energy.

K = P2/ 2m

= ∆K/K = 2(∆P/P) = 2*5 =10

2. What is the Equation of Kinetic Energy?

Ans. The numerical formula is KE = 0.5 * mv2. In the equation, m is an object’s mass and v counts velocity or rate at which the substance changes its place.

3. How Kinetic Energy Differs from Momentum?

Ans. In a constant object, momentum increases directly with speed whereas kinetic energy increases the square of the velocity due to energy momentum relation.