The resistive force increases.

The object stops accelerating and reaches terminal velocity.

The terminal velocity increases.

The object reaches terminal velocity and stops speeding up.

Air resistance increases.

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.

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.