Differential Equation direction fields

The equation for a stone falling under gravity with air resistance,

dv/dt = g - kv^2, v > 0,

where k is a constant drag coefficient. Pay particular attention to the direction along the line v = sqrt{g/k} = vt. What is the significance of vt?

Sketch solution graphs which start at t = 0,

(i) for an initial velocity > vt and

(ii) for an initial velocity < vt.

I know about putting in values to draw the direction fields, but this question has thrown many people in our class and our lecturer said it was easy, so any help would be greatly appreciated.