Question

Derive relation between kinetic Energy and Momentum.

Answer 1

Hint: The kinetic energy of an object is the energy that it possesses due to its motion. In Newtonian Mechanic, linear momentum, translation, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity.

Complete step-by-step answer:
Sometimes it's described to express the kinetic energy of a particle in terms of the momentum, that's easy enough.
The kinetic energy of an object is the energy associated with the object which is under motion. It is defined as "The energy required by a body to accelerate from rest to stated velocity.
It is a vector quantity.
Mathematically
Kinetic Energy$$={\displaystyle \frac{1}{2}}m{v}^2.............\text{ 1}$$
Where, m is the mass of the object measures in kg
V is the velocity of object measured in m/s
SI unit of kinetic Energy is Joule
Momentum $$\left(P\right)=mv...........\text{ 2}$$
Where P is the momentum
m = mass (in kg)
V = Velocity (in m/s)
Multiply and divide equation 1 RHS by M
$$K.E.={\displaystyle \frac{1}{2}}{\displaystyle \frac{m^2{v}^2}{M}}$$
Substitute P = mv
So; $$K.E.={\displaystyle \frac{1}{2}}{\displaystyle \frac{P^2}{M}}$$
The above equation gives the relation between kinetic energy and momentum which is under motion.

Note: 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 mass, whereas Kinetic energy is the product of the square of speed and half of the mass.