Drag Force & Terminal Velocity Cheat Sheet

Drag force is the resistive force a fluid, such as air or water, exerts on an object moving through it. This cheat sheet helps students connect free-body diagrams, velocity, net force, and acceleration for falling objects. It is especially useful for understanding why objects do not keep speeding up forever when they fall through air.

These ideas appear in mechanics, motion graphs, and real-world applications such as skydiving, parachutes, and vehicle design.

The most important idea is that drag force usually increases as speed increases. At low speeds, drag is often modeled as $F_d = bv$ , while at higher speeds it is commonly modeled as $F_d = \frac{1}{2}\rho C_d A v^2$ . Terminal velocity occurs when drag balances weight, so the net force is $F_{net} = 0$ and acceleration is $a = 0$ .

A clear force diagram shows weight downward and drag upward for a falling object.

Key Facts

Drag force acts opposite the direction of an object's motion through a fluid.
For slow motion through a fluid, drag can be modeled as $F_d = bv$ , where $b$ is a drag constant and $v$ is speed.
For faster motion through air, drag is often modeled as $F_d = \frac{1}{2}\rho C_d A v^2$ , where $\rho$ is fluid density, $C_d$ is drag coefficient, and $A$ is cross-sectional area.
The weight of a falling object is $F_g = mg$ , where $m$ is mass and $g$ is gravitational field strength.
Terminal velocity occurs when $F_d = F_g$ , so $F_{net} = 0$ and $a = 0$ .
If downward is positive for a falling object, the net force can be written as $F_{net} = mg - F_d$ .
Increasing area $A$ or drag coefficient $C_d$ increases drag force and lowers terminal velocity.
For quadratic drag at terminal velocity, $v_t = \sqrt{\frac{2mg}{\rho C_d A}}$ .

Vocabulary

Drag force: A resistive force exerted by a fluid that acts opposite an object's motion through the fluid.
Terminal velocity: The constant speed reached when drag force equals weight and the net force is zero.
Free-body diagram: A simplified diagram showing all external forces acting on one object.
Drag coefficient: A dimensionless value $C_d$ that describes how strongly an object's shape resists motion through a fluid.
Cross-sectional area: The effective area $A$ of an object facing the direction of motion through a fluid.
Net force: The vector sum of all forces on an object, given by $F_{net} = ma$ .

Common Mistakes to Avoid

Forgetting that drag acts opposite motion is wrong because drag changes direction if the object's velocity changes direction.
Treating terminal velocity as zero velocity is wrong because terminal velocity means constant nonzero speed with $a = 0$ .
Using $F_d = \frac{1}{2}\rho C_d A v^2$ without squaring the speed is wrong because quadratic drag depends on $v^2$ , not just $v$ .
Assuming heavier objects always fall faster is wrong because terminal velocity also depends on $A$ , $C_d$ , and the fluid density $\rho$ .
Drawing only weight in a falling-object free-body diagram with air resistance is wrong because drag must be included when air resistance is significant.

Practice Questions

1 A skydiver has mass $75\,\text{kg}$ . What is the skydiver's weight if $g = 9.8\,\text{m/s}^2$ ?
2 An object moving through air has $\rho = 1.2\,\text{kg/m}^3$ , $C_d = 0.80$ , $A = 0.50\,\text{m}^2$ , and $v = 20\,\text{m/s}$ . Calculate the drag force using $F_d = \frac{1}{2}\rho C_d A v^2$ .
3 A falling object has $m = 10\,\text{kg}$ and experiences $F_d = 60\,\text{N}$ upward. If downward is positive and $g = 9.8\,\text{m/s}^2$ , find $F_{net}$ and $a$ .
4 Explain why opening a parachute decreases a skydiver's terminal velocity even though the skydiver's mass stays the same.

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Drag Force & Terminal Velocity Cheat Sheet

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