A 1000 kg boat is traveling at 90 km/h when its engine is shut off. The magnitude of the kinetic frictional force f_k between the boat and water is proportional to the speed v of the boat: f_k = 70v, where v is in meters per second and f_k is in newtons. Find the time required for the boat to slow to 45 km/h.

Answer 1

An exact solution will require calculus, since the acceleration is not constant.

M*dV/dt = -fk = -70V
dV/V = -(70/M)dt

Since you have separated variables to opposite sides, the differential equation is easily integrated.

ln V2/V1 = -ln2 = (-70/M)T
where T is the time interval.

T= (M/70)*ln2 = (1000/70)*0.693
= 99 seconds