In inertial frame $S$ a particle moves along the $x$-axis as shown in Figure 1. Inertial frame $S'$ moves in the $+x$-direction at speed $v=0.50c$ relative to $S$ The origins of the frames coincide at $t=t'=0$ Take $c=3.00\times10^8\ \mathrm{m\,s^{-1}}$

The Lorentz transformations are

$$x'=\gamma(x-vt),\qquad t'=\gamma\left(t-\frac{vx}{c^2}\right), \qquad \gamma=\frac{1}{\sqrt{1-v^2/c^2}}.$$