(Solved): The relativistic equation of motion for a particle of constant mass m moving along the x axis under ...

The relativistic equation of motion for a particle of constant mass $m$ moving along the $x$ axis under the action of force $F$ is $\frac{d}{dt}(?m\stackrel{?}{x})=F$ where $?={\left(1?\frac{{\stackrel{?}{x}}^2}{c^2}\right)}^{?\frac{1}{2}}$ and $c$ is a constant (speed of light). If the force $F$ is a constant a. Show that the distance travelled from rest in time $t$ is given by $x=\frac{m{c}^2}{F}\left\{{\left(1+\frac{F^2{t}^2}{m^2{c}^2}\right)}^{\frac{1}{2}}?1\right\}$ b. Obtain the potential energy function via the classical definition and show that the total energy is conserved if the kinetic energy is defined by $T=?m{c}^2$.