Question

derive the formula for kinetic energy of a particle having a mass and velocity using dimensional analysis​

Answer 1

Answer: Derived in below shown pic.

A dimensionally correct formula may or may not be physically correct as in this case,

1/2do not have any dimensions

Therefore formula of kinetic energy which is dimensionally correct becomes

E=M(V)^2

But it is the same formula which was given by Einstein in vacuum

E=M(C)^2

I hope that you had found your answer.

If i am wrong at any step please let me know

Answer 2

Kinetic energy is one of the types of energy and it is defined as the energy in an object due to its virtue of motion. The dimension of kinetic energy will be the same as that of energy. Therefore, kinetic energy is measured in Joules (SI unit of energy) and its dimensional formula will be [M1L2T−2].