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## Homework Statement

A ship is traveling across the sea when its engines are cut. The ship slows down by a = -kV

^{2}. The ship gradually slows down from 5 knots/h to 12 knots/h over 20min. Determine the distance traveled in nautical miles. One knot is 1 nautical mile per hour.

## Homework Equations

Kinematics

## The Attempt at a Solution

Vi = .2 [nmiles / min]

Vf = .1167 [nmiles / min]

nmiles= nautical miles

a = dV/dt = -kV

^{2}

(1/V

^{2})dV = -k dt

integrate over Vi to Vf and 0 to 20min.

therefore k = .1786 [1/nmiles]

units seem to add up if a = -kv^2 the units will become nmiles/min^2

confident that k is correct. Not sure though.

Now for V.

a= v dv/dx = -kv

^{2}

-kv

^{2}= v dv/dx

-kdx = (1/v) dv

integrating from Xi to Xf and Vi to Vf

-k(Xf - Xi) = ln(Vf - Vi)

Natural log of a negative number, impossible.

Where am I going wrong?

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