The kinetic energy of an object is the energy associated with it when it is moving. “The energy required by a body to accelerate from rest to a stated velocity,” according to the definition. It’s a quantity with a vector.

If a body’s mass is one kilogramme and its velocity is metres per second, the kinetic energy is one kilogramme per metre squared and seconds squared.

**The formula for Kinetic Energy **

As a mathematical expression:

KE =1/2∗m∗v2

Where,

- The mass of the object in kilogrammes is denoted by m.
- v is the object’s velocity in metres per second.

Joules are the SI unit of kinetic energy.

**Momentum**

The virtue of an object’s mass is its momentum. The product of mass and velocity is what it’s called. It’s a quantity with a vector.

**The formula for gaining momentum**

A moving object’s momentum can be described mathematically as –

p=mv

Where,

- The letter p denotes the momentum.
- The mass of the object, measured in kilogrammes, is m.
- The velocity of an object is measured in metres per second (m/s).

The SI Unit of Momentum is kg.m/s

**Momentum and Velocity **

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

Moreover, momentum differs from kinetic energy as momentum is a vector having a direction, whereas kinetic energy is a scalar having no direction.

Values of kinetic energy and momentum vary at higher velocities as momentum tends to increase linearly with velocity, whereas kinetic energy increases quadratically.

Kinetic energy is directly proportional to the mass and velocity of an object, while momentum is also directly proportional to the mass and velocity of the object. So, an increase in mass increases kinetic energy and momentum in exact proportion and vice-versa.

Momentum can be calculated by multiplying the mass by velocity. The following is how it is expressed.

P = m∗v

Where m denotes a substance’s mass.

V stands for velocity.

Because momentum and kinetic energy are both affected by velocity and mass, a change in one impacts the other.

**Here are the key differences between Kinetic energy and Momentum. **

Kinetic Energy | Momentum |

Kinetic energy is always positive | Momentum can be either positive or negative |

Kinetic energy is a scalar quantity | Momentum is a vector quantity |

Kinetic energy depends quadratically on velocity | Momentum depends linearly on velocity |

Kinetic energy is conserved only in elastic collisions | Momentum is always conserved |

**Relationship between Kinetic Energy and Momentum**

When it accelerates, the energy that every substance has is known as kinetic energy, whereas momentum is defined as an object’s mass in motion. Because of their connection with mass and velocity, kinetic energy and momentum have a relationship.

It’s worth noting that if a heavy particle and a light particle both have the same momentum, the light one will have significantly greater kinetic energy. When the velocity of a light particle and a heavy particle is equal, the heavier particle has higher kinetic energy.

The following is a mathematical representation of the relationship between kinetic energy and momentum:

As a result, the kinetic energy of a body is equal to the product of its momentum and half of its velocity. The relationship between a substance’s linear momentum and kinetic energy.

Note: Students should be able to understand the physical importance of both linear momentum and kinetic energy and their units. Students must know the basic mathematical expressions for both quantities in order to obtain the required relationship by executing simple mathematical operations.

**Conclusion **

The terms momentum and kinetic energy are not interchangeable because momentum is a vector (it has a direction) while kinetic energy is a scalar (it has no direction) (does not have a direction). Momentum grows linearly with velocity, whereas kinetic energy increases quadratically. Therefore their quantities at greater speeds are not the same.

Because kinetic energy describes the overall energy associated with motion, it is considered a scalar. This means that kinetic energy has no particular direction in space. On the other hand, Momentum describes motion in a given direction and has a different value in each spatial direction.