Barrons AP Calculus - David Bock

26. (a) Since then, separating variables, Integrating gives

and, since v = 20 when t = 0, C = ln 20. Then (1) becomes ln or, solving for v,

(b) Note that v > 0 for all t. Let s be the required distance traveled (as v decreases from 20 to 5);

then

where, when v = 20, t = 0. Also, when v = 5, use (2) to get or − ln 4 = −2t. So t = ln 2.

Evaluating s in (3) gives