Given a(t), then find:
v(t+dt) = v(t) + a(t)*dt
x(t+dt) = x(t) + v(t)*dt
Now use this updated values of x and v to calculate a(t+dt) and so on...
(See section 6.5 in Serway)
Problem 6-44 set-up:
a) Terminal speed = 0.98 m/s
b) After about 0.67 s the leaf reaches 99.9 % of Vterm, when is about 1.4 m high.
The fall to the ground takes about 2.14 s, compared to 0.639 s for free fall case