Consider a particle moving in a straight line, with a point O on the line taken as origin and one direction taken as positive. Let x be the displacement of the particle at time t. The particle’s velocity equals $\dot{x}$ or dx/dt, the rate of change of x with respect to t. The velocity is positive when the particle is moving forwards (in a positive direction) and negative when moving backwards.

If we assign the unit vector i in the line’s positive direction then r = xi and the velocity is seen to be a vector equal to $\dot{x}i$.

When the motion is in two or three dimensions, vectors are used explicitly. The velocity v of a particle P with position vector r is given by $v=\text{d}r/\text{d}t=\dot{r}$. When Cartesian coordinates are used, r = xi + yj + zk, and then $\dot{r}=\dot{x}i+\dot{y}j+\dot{z}k$.

Velocity has the dimensions LT⁻¹, and the SI unit of measurement is the metre per second, abbreviated to ‘ms⁻¹’.