Growth Functions

Abstract

If you drop a ball from a given height, its velocity will increase at a constant rate called the acceleration of gravity:

$$\frac{{dv}}{{dt}} = g.$$

(17-1)

Integrating, we find that v = gt, assuming that at time t = 0, the moment at which the ball was dropped, the ball had zero velocity. Actually the velocity is itself the rate at which the altitude of the ball decreases:

$$v = - \frac{{dh}}{{dt}}$$

Since $v = gt,\tfrac{{dh}}{{dt}} = - gt$, and $h = {{h}_{0}} - \tfrac{1}{2}g{{t}^{2}}$ where h ₀ is the initial height from which the ball was dropped at time t = 0.