Find how the momentum of a particle of rest mass `m_0` depends on its kinetic energy. Calculate the momentum of a proton whose kinetic energy equals `500MeV`.

Explanation

From the formula
`E=(m_0c^2)/(sqrt(1-v^2/c^2)), p=(m_0v)/(sqrt(1-v^2//c^2))`
we find `E^2=c^2p^2+m_0^2c^4` or `(m_0c^2+T)^2=c^2p^2+m_0^2c^4`
or `T(2m_0c^2+T)=c^2p^2` i.e. `p=1/2sqrt(T(2m_0c^2+T))`