# Air resistance acting on a falling body can be taken into account by

the approximate relation for the acceleration.

a= dv/dt= g-kv, where k is a constant. A) Derive a formula for the

velocity of the body as a function of time assuming it starts from rest (v=

0 at t=0)

B) Determine an expression for the terminal velocity, which is the

maximum value the velocity reaches

Use the separation of variables integration method.

dv/(g - kv) = dt

Integrate both sides startuing from t=0, when v = 0, and you get

t = (-1/k) [log (g - kv) - log g]

-kt = log (1 - kv/g)

e^-kt = 1 - kv/g

v = (g/k) (1 - e^-kt)

When t becomes very large, v -> g/k

you suck.