Yes, the velocity of a falling object changes. While the direction of motion does not change, the magnitude of the velocity increases due to the gravitational force.
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The motion of objects falling under the influence of gravity alone is called free fall.
Objects fall towards the earth due to the gravitational force exerted by the earth.
The greater the mass of an object, the greater its inertia.
The mass of an object is a measure of its inertia.