Two point particles have equal charge $q=500$esu and different masses, $m_1=85gr$ and $m_2=15gr,$ are confined to move freely along the $x$ axis. Note that esu is the unit of electric charge when working with units of mass in grams and distance in centimeters.

The electrical force between the particles is a repelling force which is derived from the potential energy function $U(x_1,x_2)$ of the two$-$particles system. $U(x_1,x_2)$ depends only on the distance of the particles and is given by

$U(x_1,x_2)=\frac{q^2}{|x_2-x_1|}$

At $t=0$ the particle of mass $m_2$ is at rest at the origin $(x_2=0),$ and the particle of mass $m_1$ begins to move from point $x_1=-52cm$ with velocity $v_0=82c\frac{m}{s}$ towards particle $m_2.$