| ||||

| ||||

An object moving in one-dimension can be described in terms of its position $x$ and and its velocity $v_x$. If the force on the object is known, then the motion can be described by two first order differential equations,

$\large \frac{dx}{dt}=v_x$ and $\large \frac{dv_x}{dt}=a_x=F_x(x,v_x,t)/m.$

Here $F$ is the force, $m$ is the mass, and $t$ is the time. The form below can be used to numerically integrate these equations for a total number of $N_{steps}$ steps using a step size of $\Delta t$. The acceleration $a_x$ can be given as a function of $x$, $v_x$, and $t$.