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🔋college physics i – introduction review

Terminal Velocity Equation

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

The terminal velocity equation describes the maximum velocity an object can reach when falling through a fluid, such as air or water. It represents the point at which the drag force acting on the object equals the gravitational force, resulting in a constant velocity.

5 Must Know Facts For Your Next Test

  1. The terminal velocity equation is $v_t = \sqrt{\frac{2mg}{\rho A C_d}}$, where $v_t$ is the terminal velocity, $m$ is the mass of the object, $g$ is the acceleration due to gravity, $\rho$ is the density of the fluid, $A$ is the cross-sectional area of the object, and $C_d$ is the drag coefficient of the object.
  2. The terminal velocity is reached when the drag force and gravitational force on the object are equal, resulting in a constant velocity.
  3. Factors that affect terminal velocity include the object's mass, shape, and surface area, as well as the properties of the surrounding fluid, such as density and viscosity.
  4. Objects with a higher mass and smaller surface area tend to reach a higher terminal velocity, while objects with a larger surface area and lower mass will have a lower terminal velocity.
  5. Terminal velocity is an important concept in various fields, such as skydiving, ballistics, and the study of atmospheric phenomena like precipitation and dust particles.

Review Questions

  • Explain the relationship between drag force and gravitational force in the terminal velocity equation.
    • The terminal velocity equation describes the point at which the drag force acting on an object falling through a fluid exactly balances the gravitational force. At this equilibrium, the net force on the object is zero, and it reaches a constant, maximum velocity known as the terminal velocity. The equation shows that terminal velocity is determined by the balance between the object's weight (proportional to mass) and the drag force (proportional to the object's cross-sectional area and the fluid's density).
  • Analyze how the properties of an object and the surrounding fluid affect its terminal velocity.
    • The terminal velocity equation reveals that an object's mass, cross-sectional area, and the fluid's density and drag coefficient all influence its terminal velocity. Heavier objects with smaller surface areas tend to reach higher terminal velocities, as the gravitational force dominates over the drag force. Conversely, objects with larger surface areas and lower masses will have lower terminal velocities, as the drag force becomes more significant. Additionally, the properties of the surrounding fluid, such as its density and viscosity, can significantly impact the drag force and, consequently, the terminal velocity of the object.
  • Evaluate the importance of the terminal velocity equation in various real-world applications.
    • The terminal velocity equation has important applications in diverse fields, such as skydiving, ballistics, atmospheric science, and the study of particle behavior. In skydiving, the equation helps determine the maximum safe speed at which a person or object can fall, which is crucial for parachute deployment. In ballistics, it is used to calculate the trajectory and impact velocity of projectiles. In atmospheric science, the terminal velocity equation is applied to understand the behavior of precipitation, dust, and other particles suspended in the air. Additionally, the equation provides insights into the motion and sedimentation of particles in fluids, which is relevant for industrial processes and environmental studies. Overall, the terminal velocity equation is a fundamental tool for analyzing and predicting the motion of objects falling through fluids in a wide range of contexts.