Finding Time for Boat to Slow Down with Velocity Dependent Forces

[cbasst]

Homework Statement

A 1000kg boat is traveling at 25 m/s when its engine is shut off. The magnitude of the frictional force f between the boat and the 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 12.5 m/s.

Homework Equations

F=ma
a(t)=v'(t)

The Attempt at a Solution

70v = (1000 kg) * a
a(t) = 70v(t) / (1000 kg)

However, after this point I don't know what to do. I can't use the formula v² = v_o² + 2a(Δx), because I don't know Δx. I don't know how I would find the anti-derivative of a(t), since a(t) is defined in terms of v(t). What am I missing?

 

[Spinnor]

Does this look right?

 

[cbasst]

It probably is, but I don't understand it. We haven't gotten that far in ap calculus yet, so I'll ask my teacher about how that works tomorrow. Thanks for the help!