Final answer:
An object in free fall reaches terminal velocity when the force due to air resistance is equal to the gravitational force. At this point, the object falls with a constant velocity as direction and magnitude are balanced, causing no change in its motion.
Step-by-step explanation:
Velocity When Air Resistance Equals the Force of Gravity
When an object is in free fall, it experiences a constant acceleration due to gravity, which is approximately 9.81 m/s² near the Earth's surface. If air resistance is negligible, all objects fall with this acceleration regardless of their mass. However, in the real world, air resistance does affect the fall of an object. As an object accelerates due to gravity, it encounters air resistance that increases with its velocity.
At a certain velocity, the force due to air resistance equals the force of gravity acting on the object. This is known as the terminal velocity. When this state is reached, the object no longer accelerates and moves at a constant velocity. The two factors that velocity must have to cause no change in the motion of an object are direction and magnitude. The terminal velocity is significant because it represents a balance of forces where the net force is zero, resulting in no acceleration.
For an object falling in air, reaching terminal velocity means that its downward weight is exactly balanced by the upward drag force from air resistance. The object then falls at a steady speed without gaining further velocity. Understanding these conditions is crucial in areas such as parachute design and predicting the fall of objects from heights.