Let's break down the problem step by step:

Given:

• Initial velocity $v_0 = 5$ knots
• Acceleration $a = 60 \, \text{nmi/hr}^2$
• Time $t = 10 \, \text{minutes} = \frac{10}{60} \, \text{hours} = \frac{1}{6} \, \text{hours}$

Formula:

The final velocity can be found using the kinematic equation: $v = v_0 + a \cdot t$ where:

• $v$ is the final velocity
• $v_0$ is the initial velocity
• $a$ is the acceleration
• $t$ is the time

Calculation:

1. Substitute the known values into the formula: $v = 5 \, \text{knots} + 60 \, \text{nmi/hr}^2 \times \frac{1}{6} \, \text{hr}$
2. Simplify the expression: $v = 5 + 60 \times \frac{1}{6} = 5 + 10 = 15 \, \text{knots}$

Conclusion:

The velocity of the vessel at the end of the 10-minute period is 15 knots.

Would you like a deeper explanation or have any other questions?

Here are some related questions to consider:

1. What if the time was 15 minutes instead of 10 minutes?
2. How would the result change if the acceleration were negative?
3. Can you derive the distance traveled during this 10-minute interval?
4. What would happen if the initial velocity was 0?
5. How would the result change if the units were different, like meters per second?

Tip: Always ensure that units are consistent throughout the calculation, especially when converting between time or speed units!