The relativistic momentum of a particle moving with speed v is equal to:
[tex]p=\gamma m_0 v[/tex]
where
[tex]m_0[/tex] is the rest mass of the particle
[tex]\gamma= \frac{1}{ \sqrt{1- \frac{v^2}{c^2} } } [/tex] is the relativistic factor, with c being the speed of light.
The Newtonian momentum is instead
[tex]p=m_0 v[/tex]
For the particle in our problem, the relativistic momentum is 2.5 times the Newtonian momentum: this means [tex]\gamma=2.5[/tex]. If we re-arrange the formula of [tex]\gamma[/tex], we get:
[tex]v=c \sqrt{1- \frac{1}{\gamma^2} } [/tex]
and by using [tex]\gamma=2.5[/tex], we find the particle velocity:
[tex]v=(3 \cdot 10^8 m/s) \sqrt{1- \frac{1}{(2.5)^2}} =0.917 c = 2.75 \cdot 10^8 m/s[/tex]
