Hello, this is a series of related questions from my year 12 math class. Math is not my strongest subject so help with these would be appreciated. These are extra credit questions but i just can't seem to do much with them.

Objects falling vertically in a fluid medium are subject to a drag force due to the viscosity of the fluid. The magnitude of this drag force and hence its effect on the acceleration of the object is generally a function of the velocity of the object. Since the acceleration due to viscosity opposes gravity, a suitable model could be derived from the expression:

a = g - kv

where a is the acceleration of the object, v is its velocity, g the acceleration due to gravity, and k is a constant related to the viscosity of the fluid.

A. A ball-bearing sinking in a container of oil represents a suitable example of such motion. Using x for verticle displacement from the top of the fluid, t for time from th moment the ball is relased, and assuming v = 0, and x = 0 when t = 0, develop an expression for x in terms of g, k and v.

B. Develop an expression for v in terms of g, k and t

C. Develop an expression for x in terms of g, k and t

D. Theoretically, the ball bearing will never reach "Terminal Velocity". However, it is possible to compare times and depths reached for different fluids for the ball bearing to reach say 95% of its terminal velocity. By re-arranging the expressions you have already developed, or otherwise, demonstrate the effect k has on these times and depths.

If you guys like, i could also scan the page out of my textbook and atatch it but the wording should be identicle.

Thanks in advance for anyhelp !!