Question

A particle of rest mass `m_0` moves along the x axis of the frame K in accordance with the law `x=sqrt(a^2+c^2t^2)`, where `a` is a constant, c is the velocity of light, and t is time. Find the force acting on the particle in this reference frame.

Answer 1

`x=sqrt(a^2+c^2t^2)`, so `overset(.)x=v=(c^2t)/(a^2+c^2t^2)`
or, `(v)/(sqrt(1-v^2/c^2))=(c^2t)/(a)`. Thus `(d)/(dt)((m_0v)/(sqrt(1-v^2/c^2)))=(m_0c^2)/(a)=F`