A 310,000 GRT vessel needs to achieve a steady speed of 13 knots after exiting a canal. If the speed of the vessel before exiting the canal is 3 knots, calculate the time (in minutes) to reach the desired speed assuming that her acceleration is 0.08 knots per minute.
What is the distance in NM covered by the vessel during the acceleration from 3 knots to 13 knots
To calculate the time it takes for the vessel to reach the desired speed, we can use the formula:
time = (final speed - initial speed) / acceleration rate
Given:
Initial speed = 3 knots
Final speed = 13 knots
Acceleration rate = 0.08 knots per minute
time = (13 - 3) / 0.08
time = 10 / 0.08
time = 125 minutes.
So, it will take 125 minutes for the vessel to reach a speed of 13 knots.
To calculate the distance covered during the acceleration, we can use the formula:
distance = initial speed * time + (1/2) * acceleration rate * time^2
Given:
Initial speed = 3 knots
Acceleration rate = 0.08 knots per minute
Time = 125 minutes
distance = 3 * 125 + (1/2) * 0.08 * (125^2)
distance = 375 + (1/2) * 0.08 * 15625
distance = 375 + 625
distance = 1000 nautical miles.
Therefore, the vessel covers a distance of 1000 nautical miles during the acceleration from 3 knots to 13 knots.
To calculate the distance covered by the vessel during the acceleration from 3 knots to 13 knots, we can use the equation:
Distance = (Final speed^2 - Initial speed^2) / (2 * acceleration)
First, we need to convert the speeds from knots to NM (nautical miles). Since 1 knot is equal to 1.15 NM, we have:
Initial speed = 3 knots * 1.15 NM/knot = 3.45 NM
Final speed = 13 knots * 1.15 NM/knot = 14.95 NM
Acceleration = 0.08 knots/minute * 1.15 NM/knot = 0.092 NM/minute
Now we can substitute the values into the equation:
Distance = (14.95^2 - 3.45^2) / (2 * 0.092)
Calculating this, we get:
Distance ≈ 146.49 NM
Therefore, the vessel covers approximately 146.49 NM during the acceleration.