Question

what does acceleration do to the speed of an object free falling?

Answer 1

The acceleration is directly proportional to the velocity :)

Answer 2

acceleration increases the speed of the freely falling object

Answer 3

Mathematically, we define velocity as the change in position overtime - that is - the first derivate of coordinates with respect to time.

\[v = \frac{ dx }{ dt } \]

Acceleration is the change of the speed at which an object is travelling - that is - the first derivative of velocity with respect to time.

\[a = \frac{ dv }{ dt } \]

But we already said that velocity is a function of coordinates, so it turns out that acceleration is the second derivative of coordinates over time.
\[v = \frac{ d^2x }{ dt^2 } \]
We can generalize the definition as
\[a = \frac{ dv }{ dt } = \frac{ v - v _{0} }{ \Delta t }\]
and solving for v gives the law for motion
\[v = v _{0}+a* t\]
So, the answer to your question - when there is an increase in acceleration, there is an increase in velocity. For a free-falling object, acceleration causes it to fall quicker and quicker as it falls according to the equation (initial velocity is zero as it is free-fall motion)
\[v = a*t\]