Final answer:
The question involves solving a differential equation from physics, specifically modeling an object's motion with a velocity-squared drag force. While the student provided examples do not directly apply to solving the equation, steps to find classical kinetic energy are outlined. To solve the original problem, one must separate variables and integrate.
Step-by-step explanation:
The differential equation presented is m dv/dt = mg - kv^2. Here, m represents mass, g is the acceleration due to gravity, k is a resistance constant, and v is the velocity of the object. This equation models the motion of an object under the influence of gravity and a velocity-squared drag force.
To solve this equation for the velocity v as a function of time t, one can separate variables and integrate. However, since the student's question is related to a different example, involving classical kinetic energy KEclass, the provided information cannot directly solve the problem at hand.
Nonetheless, for the kinetic energy problem, one would use KEclass = 1/2mv^2 where the knowns would be plugged into this equation to find the unknown kinetic energy.
To find the velocity as a function of time for the original differential equation, you would typically proceed by rearranging the equation to separate variables and integrate, taking into account initial conditions such as initial velocity.
Over time, the velocity would approach a terminal value UT, where UT = mg/b, and b would be a constant related to k. The integration might involve an exponential decay factor indicating the approach to terminal velocity.