A force that opposes the motion of an object, slowing it down. It is velocity-dependent and acts in the opposite direction of motion.

The maximum speed an object reaches when the constant force (like gravity) and the resistive force (like air resistance) balance each other, resulting in zero net acceleration.

The time constant, $\tau = \frac{m}{k}$, indicates how quickly an object reaches terminal velocity. A larger mass or smaller k (weaker resistive force) means a longer time to reach terminal speed.

$k$ is a positive constant that depends on the shape and size of the object and the properties of the medium (like air density). It appears in the resistive force equation: $$\vec{F}_{r} = -k \vec{v}$$

At terminal velocity, the net force is zero, which means the acceleration is also zero. The object stops speeding up.

A force that opposes the motion of an object.

The maximum speed an object reaches when the constant force (like gravity) and the resistive force balance each other, resulting in zero net acceleration.

The time it takes for an object to reach approximately 63.2% of its terminal velocity; $\tau = \frac{m}{k}$.

A positive constant that depends on the shape and size of the object and the properties of the medium (like air density).

$\frac{dv}{dt} = 0$, meaning the acceleration is zero.

Without resistive forces: motion continues indefinitely (Newton's First Law) or accelerates constantly. With resistive forces: motion slows down, reaches terminal velocity, and acceleration approaches zero.

Spread-eagle: Lower terminal velocity due to greater surface area and air resistance. Streamlined dive: Higher terminal velocity due to less surface area and air resistance.

Heavier objects: Greater terminal velocities because they have a larger gravitational force to balance against air resistance. Lighter objects: Lower terminal velocities because they have a smaller gravitational force.

Initial velocity: The velocity of an object at the start of its motion. Terminal velocity: The maximum speed achieved when forces balance.

Larger mass: Longer time to reach terminal speed. Smaller k: Weaker resistive force, longer time to reach terminal speed.