A ship with a total displacement of 16 000 metric tons (1 metric ton = 1000 kg) starts from rest in still water under a constant propeller thrust T = 250 kN. The ship develops a total resistance to motion through the water given by R = 4.50v², where R is in kilonewtons and v is in meters per second. The acceleration of the ship is α = (T − R) /m, where m equals the mass of the ship in metric tons. Plot the speed v of the ship in knots as a function of the distance s in nautical miles which the ship goes for the first 5 nautical miles from rest. Find the speed after the ship has gone 1 nautical mile. What is the maximum speed which the ship can reach?