A 1000kg boat is traveling at 90km/h when its engine is shut off. The magnitude of the frictional force f between the boat and water is proportional to the speed v of the boat: f=70v where v is in meters per second and f is in newtons. Find the time required for the boat to slow to 45 km/h.(adsbygoogle = window.adsbygoogle || []).push({});

This problem wasn't assigned so I might be trying something I'm not supposed to know how to do. I have a FBD and have defined the x-axis in the direction of the boat's motion.

-f=ma=-70v

therefore v(t)=[tex]-\int .070vdt [/tex]

I wish I could show more work but I'm don't know where to go next. I think this employs some calculus I'm not familiar with so if someone could just point out a concept I need to look at I would appreciate it.

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# A boat's acceleration is proportional to its velocity

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