Force and Motion Dynamics

A skydiver is falling towards the Earth. Which of the following statements accurately describes the direction of the resistive force acting on the skydiver?

An object of mass $m$ is falling under the influence of gravity and a resistive force proportional to its velocity, given by $F_r = -kv$, where $k$ is a constant. Which of the following differential equations correctly describes the motion of the object?

A ball of mass $m$ is dropped from rest and experiences air resistance given by $F = -kv$, where $k$ is a positive constant. Given that the initial velocity is zero, what is the velocity of the ball as a function of time?

An object falls through the air, experiencing a resistive force. Which of the following changes would result in a smaller time constant ($τ$)?

A sphere of mass 2 kg falls through a fluid with a resistive force $F = -4v$, where $v$ is the velocity in m/s. What is the time constant for this system?

Under what condition does an object reach terminal velocity when falling through a fluid?

A 5 kg object falls through the air and experiences a resistive force given by $F = -2v$, where $v$ is in m/s. What is the terminal velocity of the object?

An object reaches a terminal velocity $v_t$ when falling through air. If the mass of the object is doubled, what happens to the new terminal velocity, assuming the resistive force is still proportional to velocity?

A ball is dropped from a height and reaches terminal velocity. Which of the following statements about the velocity-time graph of the ball is correct?

Which of the following acceleration-time graphs best describes the motion of an object that is dropped from rest and experiences air resistance?