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: Constant acceleration (often due to gravity), linear change in velocity. | With resistive forces: Acceleration is not constant, velocity approaches a terminal value, exponential change in velocity.

Larger time constant: Object takes longer to reach terminal velocity, either due to larger mass or smaller k. | Smaller time constant: Object reaches terminal velocity more quickly, due to smaller mass or larger k.

Spread-eagle: Larger surface area, greater air resistance, lower terminal velocity. | Streamlined dive: Smaller surface area, less air resistance, higher terminal velocity.

Feather: Lower mass, higher surface area to mass ratio, reaches terminal velocity quickly, falls slowly. | Bowling ball: Higher mass, lower surface area to mass ratio, takes longer to reach terminal velocity, falls faster.

Initial Velocity: The velocity of an object at the start of its motion, determined by external factors (e.g., how hard it was thrown). | Terminal Velocity: The constant speed that the object eventually reaches when the force of gravity is balanced by the drag force.

1. Apply Newton's Second Law ((F_{net} = ma)). 2. Set up the differential equation for velocity. 3. Use separation of variables. 4. Integrate to find the velocity function. 5. Apply initial conditions to solve for constants.

1. Set the net force equal to zero (resistive force + gravitational force = 0). 2. Solve for velocity ((v_t)), which represents terminal velocity.

1. Velocity approaches terminal velocity (constant value). 2. Acceleration approaches zero. 3. Net force approaches zero.

1. Calculate the time constant, $\tau = \frac{m}{k}$. 2. A larger mass or smaller k (weaker resistive force) means a longer time to reach terminal speed.

1. Draw a free-body diagram to identify all the forces acting on the object. 2. Write out the differential equation and then solve it step-by-step.