Displacement of Particle under Force

Theorem
Let $P$ be a particle of constant mass $m$.

Let the position of $P$ at time $t$ be specified by the position vector $\mathbf r$.

Let a force applied to $P$ be represented by the vector $\mathbf F$.

Then the motion of $P$ can be given by the differential equation:


 * $\mathbf F = m \dfrac {\d^2 \mathbf r} {\d t^2}$

or using Newtonian notation:
 * $\mathbf F = m \ddot {\mathbf r}$