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A boat of mass m is pushed away from the berth with the initial speed v0....

A boat of mass m is pushed away from the berth with the initial speed v0. Suppose that the drag force f is proportional to the velocity of the boat; the second Newton’s law implies ma = −kv where v is the velocity of the boat, a is acceleration, k > 0 is the drag coeffinient.

(a) Find the velocity of the boat as a function of time t. Your solution may involve v0, m, k as parameters.

(b) Find the distance x between the boat and the berth as a function of time. Sketch the graph of t ?→ x(t) and find limt→+∞ x(t).

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