Yes, if an object is in free fall and its initial speed is zero, it will accelerate. In the absence of any external forces such as air resistance, objects in free fall near the surface of the Earth experience a gravitational force that causes them to accelerate downward. This acceleration is often denoted as "g" and is approximately equal to 9.8 meters per second squared (m/s²) near the Earth's surface.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In the case of free fall, the net force acting on the object is the force of gravity, which can be calculated as the product of the object's mass and the acceleration due to gravity (F = m * g).
Since the initial speed is zero, the object's velocity starts from rest. As time progresses, the object's velocity will increase because of the gravitational force acting on it. Therefore, the object will undergo continuous acceleration during its free fall.
It's important to note that in the real world, factors such as air resistance can affect the motion of objects in free fall. However, in ideal conditions with negligible air resistance, an object in free fall will accelerate even if its initial speed is zero.