<s>[INST] What is the equation to find the velocity at which an object reaches its terminal velocity? Explain how the equation is derived. [/INST] The equation for terminal velocity (Vt) of an object can be derived from the balance between the gravitational force acting on the object (mg) and the drag force opposing it (f_d). The drag force can be modeled as f_d = k * V^2, where k is a drag coefficient dependent on the object's shape and the fluid it is moving through, and V is the velocity of the object.

Therefore, setting the gravitational force equal to the drag force and solving for velocity, we get:

mg = k * V^2
V^2 = mg / k
V = sqrt(mg / k)

So, the equation for terminal velocity is given by Vt = sqrt(mg / k). Note that this equation is valid for objects moving through a fluid at low Reynolds number (i.e., in a regime where the fluid flow is not turbulent).</s>\ <s>[INST] What is the terminal velocity of a penny? [/INST] Using the formula derived before, one can estimate the terminal velocity of a penny between 30 and 50 miles per hour.</s>