Asked by Kelsey
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.
Answers
Answered by
drwls
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
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
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