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## Homework Statement

A boat of mass 1000 kg is moving at 25 m/s. The friction force ##f## is proportional to the speed ##v## of the boat, ##f = 70v##. How many time will take for the boat to reduce its speed to 12.5 m/s?

## Homework Equations

##\vec{F_r} = m \vec{a_r}##

## The Attempt at a Solution

Since ##f## is proportional to ##v## at each instant ##t##, I integrated ##f## to get the total force.

$$f_{\text{total}} = \int_{v_o}^{v_f}-70vdv$$

the minus sign is because that force is opposite to the movement.

Then, I assumed that the total force equals the mass times the total acceleration. Next, I substituted the value for the total acceleration from the above expression and I used it in the equation: ##V = V_o + at## to get the total time ##t##. Is this correct?