Physics · Fluids

Drag and Terminal Velocity

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Wrap-up

What you learned

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Read next: Projectile MotionCompare free-flight and drag-limited motion

Key takeaway

Drag starts small because the object starts with little speed, then grows rapidly as the fall speeds up.
Weight stays constant while drag changes, so the net force is largest early and much smaller near terminal speed.

Common misconception

Terminal velocity happens because gravity turns off after the object has been falling for a while.

Gravity is still acting; the weight force stays essentially constant in this model.

Connect drag to force balance next

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Compare free-flight and drag-limited motionMechanics

Projectile Motion

Launch a projectile, watch the trajectory form, and connect the range, height, and component motion to the launch settings.

Stay with one-fluid speed bookkeepingFluids

Continuity Equation

Keep one steady stream tube on screen and use Q = Av to connect cross-sectional area, flow speed, and the same volume flow rate through narrow and wide sections.

Carry fluid speed into pressure tradeoffsFluids

Bernoulli's Principle

Follow one steady ideal-flow pipe and see how pressure, speed, and height trade within the same Bernoulli budget while continuity keeps the flow-rate story honest.

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Reference and support

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Equation snapshotQuadratic drag for this bounded model · WeightShow 2 equations

Quadratic drag for this bounded model
$F_{d} = k A v^{2}$
In this bounded model, drag gets much larger as speed increases.
Weight
$W = m g$
Gravity keeps the downward weight essentially constant while the object falls.

Why it behaves this way

Explanation

This page follows one object released from rest through one fluid. The downward weight stays fixed at $m g$ , while the upward drag force starts near zero and grows with speed according to $F_{d} = k A v^{2}$ . That changing force balance is why the fall does not behave like constant-acceleration free fall.

Terminal velocity is the speed where drag has grown enough to balance the weight. The object does not stop there. It keeps moving downward, but once drag and weight are nearly equal, the net force is near zero, so the speed stops increasing much.

Each control changes a different part of that balance. More mass increases the weight, so a higher speed is needed before drag can match it. More area or a larger drag-strength constant makes drag stronger at the same speed, so the object reaches balance sooner and at a lower terminal speed.

Key ideas

01Drag starts small because the object starts with little speed, then grows rapidly as the fall speeds up.

02Weight stays constant while drag changes, so the net force is largest early and much smaller near terminal speed.

03Terminal velocity means drag and weight are balancing, so acceleration becomes nearly zero.

04At terminal velocity the object is still moving downward; what fades is the change in speed, not the motion itself.

05A larger mass raises terminal speed, while a larger area or stronger drag lowers it.

Worked examples

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the live bench values. First predict the terminal speed from the current controls, then use the current time and speed to read the live force balance.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current setup with $m = 2$ , $A = 0.05$ , and $k = 12$ , what terminal speed does this drag model predict?

m

Mass

2 kg

A

Area

0.05 m²

k

Drag strength

W

Weight

19.6 N

1. Turn the mass into the constant weight

With gravity fixed on this page, the current setup gives

W = m g = 19.6 N

2. Use the force-balance condition for terminal speed

Terminal speed is where drag catches the weight, so

k A v_{t}^{2} = m g

with

k = 12

and

A = 0.05 m^{2}

3. Solve for the speed where drag matches weight

That gives

v_{t} = m g / (k A) = 5.72 m/s

for the current controls.

Predicted terminal speed

W = 19.6 N, v_{t} = 5.72 m/s

This setup sits in the middle, so the balance speed is neither especially low nor especially high.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows one object falling through one fluid column with a distance ruler on the left and a readout card on the right. The object width changes with area, while mass is represented through the force readouts rather than by resizing the object. Optional overlays show a constant downward weight arrow, an upward drag arrow that grows with speed, a net-force arrow, a terminal-speed cue, and a distance guide.

The time rail controls one bounded fall from rest. Compare mode can ghost a second setup behind the current one so two force-balance stories stay on the same scale.

The readout card reports mass, area, drag strength, distance fallen, current speed, terminal speed, drag force, and net downward force.

Graph summary

The speed-history graph is the main motion graph. The speed rises quickly and then bends toward the constant terminal-speed line.

The force-balance graph keeps the forces explicit: weight stays flat, drag rises, and the net downward force falls toward zero.

The response graphs isolate mass, area, and drag strength. The mass sweep rises, while the area and drag-strength sweeps fall because stronger drag-side factors lower terminal speed.

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Starter track

Step 5 of 5

Fluid and Pressure

Drag and Terminal Velocity appears later in this track, so it is cleaner to start from the beginning first.

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