Determine The Final Velocity Of A Boat That Starts At $2.5 \, \text{m/s}$ And Accelerates At $2.5 \, \text{m/s}^2$ For $8.5$ Seconds.

Introduction

In this article, we will explore the concept of final velocity and how to calculate it using the equation of motion. We will use a real-world example of a boat accelerating from an initial velocity to a final velocity. The equation of motion is a fundamental concept in physics that describes the relationship between an object's position, velocity, and acceleration.

Equation of Motion

The equation of motion is given by:

$$v = u + at$$

where:

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

Given Values

We are given the following values:

• Initial velocity ($u$): $2.5 \, \text{m/s}$
• Acceleration ($a$): $2.5 \, \text{m/s}^2$
• Time ($t$): $8.5$ seconds

Calculating the Final Velocity

We can now plug in the given values into the equation of motion to calculate the final velocity:

$$v = u + at$$

$$v = 2.5 \, \text{m/s} + (2.5 \, \text{m/s}^2)(8.5 \, \text{s})$$

$$v = 2.5 \, \text{m/s} + 21.25 \, \text{m/s}$$

$$v = 23.75 \, \text{m/s}$$

Discussion

The final velocity of the boat is $23.75 \, \text{m/s}$. This means that the boat will be traveling at a speed of $23.75 \, \text{m/s}$ after $8.5$ seconds of acceleration.

Real-World Applications

The concept of final velocity is crucial in many real-world applications, such as:

• Aerospace Engineering: Final velocity is an important factor in the design of aircraft and spacecraft, as it determines the speed at which the vehicle will reach its destination.
• Automotive Engineering: Final velocity is also important in the design of cars, as it determines the speed at which the vehicle will reach its destination.
• Sports: Final velocity is an important factor in many sports, such as football, basketball, and tennis, as it determines the speed at which the ball will travel.

Conclusion

In conclusion, we have calculated the final velocity of a boat that starts at $2.5 \, \text{m/s}$ and accelerates at $2.5 \, \text{m/s}^2$ for $8.5$ seconds. The final velocity is $23.75 \, \text{m/s}$. This calculation is an example of how the equation of motion can be used to solve real-world problems.

Additional Resources

For more information on the equation of motion and its applications, please refer to the following resources:

• Textbooks: "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca
• Online Resources: Khan Academy, Physics Classroom
• Research Papers: "The Equation of Motion" by J. R. Taylor, "The Physics of Sports" by J. R. Taylor

Final Velocity Formula

The final velocity formula is:

$$v = u + at$$

where:

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

Example Problems

1. A car starts from rest and accelerates at $5 \, \text{m/s}^2$ for $10$ seconds. What is the final velocity of the car?
2. A ball is thrown upwards with an initial velocity of $20 \, \text{m/s}$. What is the final velocity of the ball after $5$ seconds?
3. A boat starts at $10 \, \text{m/s}$ and accelerates at $2 \, \text{m/s}^2$ for $15$ seconds. What is the final velocity of the boat?

Answer Key

1. $50 \, \text{m/s}$
2. $-20 \, \text{m/s}$
3. $35 \, \text{m/s}$
   Determine the Final Velocity of a Boat: Q&A =============================================

Introduction

In our previous article, we explored the concept of final velocity and how to calculate it using the equation of motion. We used a real-world example of a boat accelerating from an initial velocity to a final velocity. In this article, we will answer some frequently asked questions related to final velocity and the equation of motion.

Q: What is the equation of motion?

A: The equation of motion is a fundamental concept in physics that describes the relationship between an object's position, velocity, and acceleration. It is given by:

$$v = u + at$$

where:

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

Q: What is the difference between initial velocity and final velocity?

A: The initial velocity is the velocity of an object at the beginning of a time interval, while the final velocity is the velocity of the object at the end of the time interval.

Q: How do I calculate the final velocity of an object?

A: To calculate the final velocity of an object, you need to know the initial velocity, acceleration, and time. You can use the equation of motion to calculate the final velocity:

$$v = u + at$$

Q: What is the unit of final velocity?

A: The unit of final velocity is the same as the unit of velocity, which is typically meters per second (m/s).

Q: Can I use the equation of motion to calculate the final velocity of an object that is decelerating?

A: Yes, you can use the equation of motion to calculate the final velocity of an object that is decelerating. Simply use a negative acceleration value.

Q: What is the relationship between final velocity and acceleration?

A: The final velocity of an object is directly proportional to the acceleration and time, and inversely proportional to the initial velocity.

Q: Can I use the equation of motion to calculate the final velocity of an object that is moving in a circular path?

A: No, the equation of motion is only applicable to objects that are moving in a straight line. If the object is moving in a circular path, you need to use a different equation, such as the equation of circular motion.

Q: What is the significance of final velocity in real-world applications?

A: Final velocity is an important factor in many real-world applications, such as aerospace engineering, automotive engineering, and sports.

Q: Can I use the equation of motion to calculate the final velocity of an object that is moving in a non-uniform acceleration?

A: No, the equation of motion is only applicable to objects that are moving in a uniform acceleration. If the acceleration is non-uniform, you need to use a different equation, such as the equation of motion with a variable acceleration.

Conclusion

In conclusion, we have answered some frequently asked questions related to final velocity and the equation of motion. We hope that this article has provided you with a better understanding of the concept of final velocity and how to calculate it using the equation of motion.

Additional Resources

For more information on the equation of motion and its applications, please refer to the following resources:

• Textbooks: "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca
• Online Resources: Khan Academy, Physics Classroom
• Research Papers: "The Equation of Motion" by J. R. Taylor, "The Physics of Sports" by J. R. Taylor

Final Velocity Formula

The final velocity formula is:

$$v = u + at$$

where:

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

Example Problems

1. A car starts from rest and accelerates at $5 \, \text{m/s}^2$ for $10$ seconds. What is the final velocity of the car?
2. A ball is thrown upwards with an initial velocity of $20 \, \text{m/s}$. What is the final velocity of the ball after $5$ seconds?
3. A boat starts at $10 \, \text{m/s}$ and accelerates at $2 \, \text{m/s}^2$ for $15$ seconds. What is the final velocity of the boat?

Answer Key

1. $50 \, \text{m/s}$
2. $-20 \, \text{m/s}$
3. $35 \, \text{m/s}$