1. The problem statement, all variables and given/known data A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the frictional force fk between the boat and the water is proportional to the speed v of the boat: fk = 70v, where v is in meters per second and fk is in newtons. Find the time required for the boat to slow to 45 km/h. 2. Relevant equations F = ma, fk = 70v, fk = [tex]\mu[/tex]kFN, and various kinematic equations. 3. The attempt at a solution First, I calculated a0 and af by substituting v0 and vf into fk = ma = 70v, respectively. I then calculated the average acceleration by adding the initial and final accelerations together and dividing by two. Finally, I solved the equation vf = v0 + aavgt for t. The answer I got was 9.5 s, which seemed reasonable to me. However, the back of my textbook has 9.9 s for the answer. I have a suspicion that there is a more accurate way to go about treating the acceleration than by just finding an average term. After playing around with equations for over an hour though, I'm stumped. What is the correct method for solving this problem?