For a moving particle (mass m, velocity v) having a momentum p, which one of the following correctly describes the kinetic energy of the particle?

Options

A. `p^2/(2m)`
B. `p/(2m)`
C. `v^(2)/(2m)`
D. `v/(2m)`

Answer

A

Explanation

The kinetic energy of the particle is
`K=1/2 mv^2`
As momentum, p=mv or `p^2=m^2 v^2 "or" v^2=p^2/m^2`
`therefore K=1/2m(p^2/m^2)=p^2/(2m)`