ll of mass m is thrown vertically upward with an initial speed of v0. It experiences a force of air resistance given by F = - kv, where k is a positive constant. The positive direction for all vector quantities is upward. The differential equation for determining the instantaneous speed v of the ball in terms of time t as the ball moves upward is

the diferencial equation is

dv (t) / dt + (k/m) v (t) + g = 0

Explanation:

the differential equation for determining the instantaneous speed can be found from Newton's second law:

F = m*a

F drag + F gravity = m*a

(-k*v) + (-m*g) = m*a, where g is acceleration due to gravitational force

since a = dv/dt and dividing both sides by m

dv (t) / dt = - g - k/m v (t)

or

dv (t) / dt + (k/m) v (t) + g = 0