Define terminal velocity.

Terminal velocity is the maximum velocity that a falling object can reach when the resistance of the medium it is falling through equals the force of gravity.

When an object falls through a fluid, such as air or water, it experiences two opposing forces: the force of gravity pulling it downwards and the resistance of the fluid pushing against it. Initially, the force of gravity is greater than the resistance, so the object accelerates downwards. However, as the object gains speed, the resistance of the fluid increases until it eventually equals the force of gravity. At this point, the object stops accelerating and continues to fall at a constant speed, known as the terminal velocity.

The terminal velocity of an object depends on its mass, size, shape, and the properties of the fluid it is falling through. It can be calculated using the following formula:

v = √(2mg/ρACd)

where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and Cd is the drag coefficient, which depends on the shape of the object.

For example, suppose a spherical object with a mass of 0.1 kg and a diameter of 0.05 m is falling through air with a density of 1.2 kg/m³. The drag coefficient for a sphere is approximately 0.47. Using the formula above, we can calculate the terminal velocity as follows:

v = √(2 × 0.1 × 9.81 / (1.2 × π × 0.025² × 0.47)) ≈ 7.8 m/s

Therefore, the terminal velocity of the object is approximately 7.8 m/s when falling through air.