(a) (1) Make $a$ The Subject Of The Formula V = U + A T V = U + At V = U + A T .

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Introduction

In physics and mathematics, the formula $v = u + at$ is a fundamental equation that describes the relationship between an object's velocity, initial velocity, acceleration, and time. This equation is a cornerstone of kinematics, and understanding how to manipulate it is crucial for solving problems in various fields, including physics, engineering, and mathematics. In this article, we will focus on making $a$ the subject of the formula $v = u + at$, which involves isolating the acceleration term.

Understanding the Formula

The formula $v = u + at$ is a linear equation that relates the final velocity $v$, initial velocity $u$, acceleration $a$, and time $t$. The equation can be rewritten as:

$$v - u = at$$

This equation shows that the change in velocity ($v - u$) is equal to the product of the acceleration and time.

Isolating the Acceleration Term

To make $a$ the subject of the formula, we need to isolate the acceleration term on one side of the equation. This can be done by dividing both sides of the equation by $t$:

$$\frac{v - u}{t} = a$$

This equation shows that the acceleration $a$ is equal to the change in velocity divided by the time.

Example

Let's consider an example to illustrate how to make $a$ the subject of the formula. Suppose we have an object that starts from rest ($u = 0$) and accelerates to a final velocity of $v = 20$ m/s in a time of $t = 5$ s. We can use the formula $v = u + at$ to find the acceleration $a$:

$$20 = 0 + a(5)$$

Simplifying the equation, we get:

$$20 = 5a$$

Dividing both sides by $5$, we get:

$$a = 4$$

This means that the acceleration of the object is $4$ m/s$^2$.

Conclusion

In conclusion, making $a$ the subject of the formula $v = u + at$ involves isolating the acceleration term on one side of the equation. This can be done by dividing both sides of the equation by $t$. The resulting equation shows that the acceleration $a$ is equal to the change in velocity divided by the time. By following the steps outlined in this article, you can easily make $a$ the subject of the formula and solve problems involving kinematics.

Applications

The formula $v = u + at$ has numerous applications in various fields, including:

• Physics: The formula is used to describe the motion of objects under the influence of forces, such as gravity, friction, and thrust.
• Engineering: The formula is used to design and optimize systems, such as vehicles, aircraft, and spacecraft.
• Mathematics: The formula is used to solve problems involving kinematics, dynamics, and calculus.
• Computer Science: The formula is used in computer simulations and modeling of physical systems.

Tips and Tricks

Here are some tips and tricks to help you make $a$ the subject of the formula:

• Use algebraic manipulation: Use algebraic techniques, such as addition, subtraction, multiplication, and division, to isolate the acceleration term.
• Use inverse operations: Use inverse operations, such as dividing by $t$ to isolate the acceleration term.
• Check your units: Make sure that your units are consistent and that the acceleration term has the correct units.
• Practice, practice, practice: Practice making $a$ the subject of the formula by working through examples and exercises.

Common Mistakes

Here are some common mistakes to avoid when making $a$ the subject of the formula:

• Forgetting to isolate the acceleration term: Make sure to isolate the acceleration term on one side of the equation.
• Using incorrect algebraic manipulation: Use correct algebraic techniques to isolate the acceleration term.
• Not checking units: Make sure that your units are consistent and that the acceleration term has the correct units.
• Not practicing: Practice making $a$ the subject of the formula by working through examples and exercises.

Conclusion

In conclusion, making $a$ the subject of the formula $v = u + at$ involves isolating the acceleration term on one side of the equation. This can be done by dividing both sides of the equation by $t$. The resulting equation shows that the acceleration $a$ is equal to the change in velocity divided by the time. By following the steps outlined in this article, you can easily make $a$ the subject of the formula and solve problems involving kinematics.

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Introduction

In our previous article, we discussed how to make $a$ the subject of the formula $v = u + at$. In this article, we will provide a Q&A section to help you better understand the concept and address any questions you may have.

Q: What is the formula $v = u + at$ used for?

A: The formula $v = u + at$ is used to describe the relationship between an object's velocity, initial velocity, acceleration, and time. It is a fundamental equation in kinematics and is used to solve problems involving motion under the influence of forces.

Q: How do I make $a$ the subject of the formula?

A: To make $a$ the subject of the formula, you need to isolate the acceleration term on one side of the equation. This can be done by dividing both sides of the equation by $t$.

Q: What is the difference between $v$ and $u$ in the formula?

A: $v$ represents the final velocity of the object, while $u$ represents the initial velocity of the object.

Q: What is the unit of acceleration?

A: The unit of acceleration is typically measured in meters per second squared (m/s$^2$).

Q: Can I use the formula $v = u + at$ to solve problems involving circular motion?

A: No, the formula $v = u + at$ is only applicable to problems involving linear motion. For problems involving circular motion, you will need to use a different formula.

Q: How do I check my units when using the formula $v = u + at$?

A: When using the formula $v = u + at$, make sure that your units are consistent. For example, if you are using meters per second (m/s) for velocity, you should also use meters per second squared (m/s$^2$) for acceleration.

Q: Can I use the formula $v = u + at$ to solve problems involving objects moving at constant velocity?

A: No, the formula $v = u + at$ is only applicable to problems involving objects that are accelerating. For problems involving objects moving at constant velocity, you will need to use a different formula.

Q: How do I isolate the acceleration term on one side of the equation?

A: To isolate the acceleration term on one side of the equation, you can divide both sides of the equation by $t$. This will give you the acceleration term on one side of the equation.

Q: Can I use the formula $v = u + at$ to solve problems involving objects moving in three dimensions?

A: No, the formula $v = u + at$ is only applicable to problems involving objects moving in one dimension. For problems involving objects moving in three dimensions, you will need to use a different formula.

Q: How do I check my work when using the formula $v = u + at$?

A: When using the formula $v = u + at$, make sure to check your work by plugging in the values you have used into the equation and verifying that the result is correct.

Q: Can I use the formula $v = u + at$ to solve problems involving objects moving at relativistic speeds?

A: No, the formula $v = u + at$ is only applicable to problems involving objects moving at non-relativistic speeds. For problems involving objects moving at relativistic speeds, you will need to use a different formula.

Conclusion

In conclusion, the formula $v = u + at$ is a fundamental equation in kinematics that describes the relationship between an object's velocity, initial velocity, acceleration, and time. By following the steps outlined in this article, you can easily make $a$ the subject of the formula and solve problems involving kinematics. If you have any further questions, please don't hesitate to ask.

Tips and Tricks

Here are some additional tips and tricks to help you make $a$ the subject of the formula:

• Use algebraic manipulation: Use algebraic techniques, such as addition, subtraction, multiplication, and division, to isolate the acceleration term.
• Use inverse operations: Use inverse operations, such as dividing by $t$ to isolate the acceleration term.
• Check your units: Make sure that your units are consistent and that the acceleration term has the correct units.
• Practice, practice, practice: Practice making $a$ the subject of the formula by working through examples and exercises.

Common Mistakes

Here are some common mistakes to avoid when making $a$ the subject of the formula:

• Forgetting to isolate the acceleration term: Make sure to isolate the acceleration term on one side of the equation.
• Using incorrect algebraic manipulation: Use correct algebraic techniques to isolate the acceleration term.
• Not checking units: Make sure that your units are consistent and that the acceleration term has the correct units.
• Not practicing: Practice making $a$ the subject of the formula by working through examples and exercises.