Motion with constant velocity

An object moving in 3 dimensions with constant velocity ${\bf v}$ possesses a vector displacement of the form

$${\bf r}(t) = {\bf r}_0 + {\bf v} t,$$ (61)

where the constant vector ${\bf r}_0$ is the displacement at time $t=0$. Note that $d{\bf r}/dt = {\bf v}$ and $d^2{\bf r}/dt^2={\bf0}$, as expected. As illustrated in Fig. 14, the object's trajectory is a straight-line which passes through point ${\bf r}_0$ at time $t=0$ and runs parallel to vector ${\bf v}$.

Figure 14: Motion with constant velocity