2. A loaded barge has a mass of 1500000 kg and is traveling at 3m/s If a tugboat applies an opposing force of 12000 N for 10 s, what is its final velocity? How long will it take to stop the barge?How much force would a tugboat need to apply to stop it in one minute?

To solve this problem, we can use the concepts of momentum and Newton's second law.1. **Final velocity after 10 seconds:** The initial momentum of the barge is given by: The force applied by the tugboat is 12000 N in the opposite direction, so the change in momentum over 10 seconds is: The final momentum is: The final velocity is: 2. **Time to stop the barge:** To find the time it takes to stop the barge, we need to calculate how long it takes for the velocity to reach zero with a constant opposing force of 12000 N. Using the formula , where is the acceleration: The time to stop the barge from an initial velocity of 3 m/s is: 3. **Force needed to stop the barge in one minute (60 seconds):** If the barge needs to be stopped in 60 seconds, we use the same formula for acceleration: The required force is: Therefore, a force of 75000 N in the opposite direction is needed to stop the barge in one minute.