Question

When a 644 lb boat is moving at 10fps, the motor conks out. How much farther will the boat
glide, assuming its resistance to motion is 2v lb where v is in fps.

Answer 1

Well, the last time I did this in pounds and slugs was about 1956 but
in your units g = 32 ft/s^2 approximately
m = mass of boat in slugs = weight / g = 644/32 = 20.1 slugs
F = m a
2 v = -20.1 a = -20.1 dv/dt
2 v + 20.1 dv/dt = 0
let v = A e^kt
then dv/dt = k A e^kt = k v
2 v + 20.1 k v = 0
k = -2/20.1 = - 1/10 approx
v = Vi e^-t/10 = 10 e^-t/10
well it goes slower and slower but never hits zero
let's look at 10 seconds
v at 10 = 10 e^-1 = 3.7
look at 60 seconds
v at 60 = 10 e^-6 = 0.025 well that is pretty near zero :)

Answer 2

Oh forgot you want x
x = -100 e^-t/10 + c
if c = 100
then x = 0 at 0 and 100 at t = infinity