Final answer:
A body dropped from rest in a viscous medium achieves terminal velocity when the upward drag force equals the downward gravitational force, resulting in zero acceleration and the body continuing to fall at a constant speed. The terminal velocity depends on factors like the object's size and shape, as well as the fluid's viscosity and density.
Step-by-step explanation:
When a body is dropped from rest in a viscous medium, it undergoes a process where its velocity increases due to gravity, but the rate of acceleration gradually decreases due to increased viscous resistance. The viscous drag force that acts on the falling object is directly related to the speed of the object and the fluid's viscosity. Simultaneously, a buoyant force acts upward, related to the fluid's density and the object's volume.
As the object accelerates, the drag force continues to grow until it equals the object's weight (gravitational force), leading to zero acceleration. Once this balance is achieved, the body continues to fall at a constant velocity, known as terminal velocity. Factors that influence terminal velocity include the object's size, shape, and density, as well as the density and viscosity of the fluid.
An example provided involves a skydiver; in a pike position, a skydiver presents a smaller cross-sectional area to the airflow, resulting in a higher terminal velocity than if the skydiver were to fall with limbs outspread. In practical applications, terminal velocity concepts are essential for understanding the motion of various objects through fluids, such as sand particles in water or cells in a centrifuge.