Q15 (b) (i)

A particle of unit mass is thrown vertically downwards with an initial velocity of $v_0$. It experiences a resistive force of magnitude $kv^2$, where $v$ is its velocity. Taking downwards as the positive direction, the equation of motion of the particle is given by

$$\ddot{x}=g-kv^2.$$

Let $V$ be the terminal velocity of the particle.

Explain why

$$V=\sqrt{\frac{g}{k}}.$$