Yes, if an object is in free fall and its initial speed is zero, it will accelerate due to the force of gravity. In the absence of any other forces (such as air resistance), all objects near the surface of the Earth experience a gravitational acceleration of approximately 9.8 meters per second squared (m/s²) downward. This means that every second, the object's velocity will increase by 9.8 m/s.
The acceleration due to gravity causes the object's speed to increase over time, so it will be moving faster and faster as it falls. The acceleration remains constant throughout the free fall, assuming there are no other influences like air resistance or wind.
It's important to note that this acceleration occurs regardless of the object's mass. In the absence of other factors, all objects, regardless of their mass, fall with the same acceleration due to gravity. This concept is known as the equivalence principle and was famously demonstrated by Galileo's experiments on falling objects.