1. The problem statement, all variables and given/known data A ship is travelling across the sea when its engines are cut. The ship slows down by a = -kV2. 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. 2. Relevant equations Kinematics 3. The attempt at a solution Vi = .2 [nmiles / min] Vf = .1167 [nmiles / min] nmiles= nautical miles a = dV/dt = -kV2 (1/V2)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 = -kv2 -kv2 = 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?