What is the solution for the laminar flow problem?

[dinkadink]

Problem:
Two horses pull a barge from rest in a canal filled with a viscous fluid that provides laminar resistance (FR = –kv). The two horses walk on each side of the canal so that their net force is applied exactly forward. The barge has a mass of 3000 kg and the donkeys pull forward with a constant net forward force of 300 Newtons.

a. If the maximum attainable speed by the barge is 2.5 m/s, what is the resistive coefficient, k (include units)?
b. How long does it take the barge to reach a speed of 1 m/s?

Once the barge reaches 2.5 m/s, at a certain time (call it t = 0) the horses instantaneously stop pulling, and the barge is allowed to drift forward.

c. How long does it take for the barge to slow to 1 m/s?
d. How far does the barge drift before coming to rest?
e. In principle, how long does it take for the barge to come to rest? Briefly explain.
f. Estimate how long it takes for the bar to be, for all practical purposes, at rest. Discuss how you decided on this estimate.

Equations:
F=-kv

Attempt at a solution:
I know how to do the integrations of the laminar flow F=-kv. Other than that I really don't know how to do this.

 

[quantumdude]

Let's start with part a. Please set up Newton's second law, solve for v(t), and post your findings.