When an object falls to Earth from a great height, its speed, in certain mathematical models, tends to a value called its terminal speed. One possible mathematical model gives the equation $m\ddot{r}=-mgj-cṙ$, where m is the mass of the particle and j the unit vector in the direction vertically upwards. The second term on the right-hand side, in which c is a positive constant, arises from the air resistance. The velocity corresponding to $\ddot{r}=0$ is equal to (−mg/c)j, which is called the terminal velocity. The terminal speed is the magnitude mg/c of this velocity. If, instead, the equation $m\ddot{r}=-mgj-c|ṙ|ṙ$ is used, the terminal speed is $\sqrt{mg/c}$ and the terminal velocity is $-\sqrt{mg/c}j$. As the particle falls, its velocity tends to the terminal velocity as t increases, irrespective of the initial conditions.