When a body falls through a fluid such as air or water, it eventually reaches a constant maximum speed at which the downward force of gravity is balanced by the upward drag force. This constant maximum speed is called the terminal velocity. Once terminal velocity is reached, how does this speed behave with time?

Introduction / Context:

When objects fall through fluids like air or water, they do not always keep accelerating indefinitely. Instead, they often reach a steady speed called terminal velocity, where the net force on the object becomes zero. This is an important concept in fluid mechanics and everyday phenomena such as raindrops falling or parachutes opening. The question asks how this terminal velocity behaves once it has been reached.

Given Data / Assumptions:

• The body is falling under gravity through a fluid (for example, air).
• As speed increases, the drag force (air resistance) increases.
• At terminal velocity, the downward weight is exactly balanced by the upward drag force.
• We consider the ideal situation where conditions like fluid density remain constant.

Concept / Approach:

Initially, when the object starts falling, its speed is small and air resistance is negligible compared with gravity, so the net force equals its weight, and it accelerates downward. As the speed increases, the drag force opposing motion increases. Eventually, a speed is reached at which the drag force becomes equal to the weight of the object. At this point, the net force is zero, so according to Newton second law, the acceleration becomes zero. With zero acceleration, the velocity no longer changes with time. This constant speed is the terminal velocity, and by definition it remains constant as long as conditions do not change.

Step-by-Step Solution:

Verification / Alternative check:

A skydiver jumping from a plane initially accelerates quickly. As his or her speed rises, air resistance increases until it balances weight, at which point the skydiver falls at a nearly constant speed. This constant speed is observed for a significant time before the parachute opens. The observed motion is clear evidence that terminal velocity, once attained, is approximately constant, rather than increasing or decreasing continuously.

Why Other Options Are Wrong:

Option A (first increases before decreasing to zero): This would imply that the falling object eventually comes to rest while still in the fluid, which does not happen in a simple fall under gravity and drag alone.

Option C (first decreases before increasing again): There is no reason for speed to decrease and then increase again once terminal conditions are met; the net force remains zero unless external conditions change.

Option D (always keeps on increasing): This would mean the object accelerates forever, which contradicts the balancing of forces at terminal velocity.

Option E (oscillates up and down continuously): There is no mechanism to cause such oscillations in simple vertical free fall with drag; the forces reach a steady balance.

Common Pitfalls:

A common misunderstanding is to think that as long as gravity acts, the object must keep accelerating. This is not correct when there is a significant opposing force like air resistance. The key idea is that acceleration depends on the net force, not just on gravity. Once drag grows enough to cancel gravity, the net force becomes zero, and the speed stops changing. Remember that terminal velocity is defined precisely as the constant speed reached when the net force and acceleration both become zero.

Final Answer:

Once terminal velocity is reached, the speed remains constant.