- #1
trojansc82
- 60
- 0
Homework Statement
Under some circumstances a falling body B of mass m encounters air resistance proportional to its instantaneous velocity v. Use Newton's second law to find the differential equation for the velocity of v of the body at time t. Recall that acceleration a = dv/dt. Assume in this case that the positive direction is downward.
Homework Equations
F = ma
a = dv/dt
air resistance = kv
kv = mg
The Attempt at a Solution
kv = mg (dv/dt)
(dv/dt) (k/m) v = g
The solution in the text is (dv/dt) + (k/m) v = g.
I'm failing to understand why (dv/dt) is added to (k/m).