A Bike Accelerates Uniformly From Rest To A Speed Of $7.10 \, \text{m/s}$ Over A Distance Of $35.4 \, \text{m}$. Determine The Acceleration Of The Bike.

Introduction

When a bike accelerates uniformly from rest to a certain speed, it covers a specific distance in a given time. The acceleration of the bike is a measure of how quickly its speed changes. In this article, we will discuss how to determine the acceleration of a bike that accelerates uniformly from rest to a speed of $7.10 , \text{m/s}$ over a distance of $35.4 , \text{m}$.

Understanding Uniform Acceleration

Uniform acceleration is a type of motion where an object's speed changes at a constant rate. This means that the acceleration of the object remains the same throughout the motion. In the case of a bike accelerating uniformly from rest, the acceleration is constant, and the speed of the bike increases at a constant rate.

Kinematic Equations

To determine the acceleration of the bike, we can use the kinematic equations of motion. The kinematic equations are a set of equations that describe the motion of an object under the influence of a constant acceleration. The three main kinematic equations are:

• $$v^2 = u^2 + 2as$$

• $$s = ut + \frac{1}{2}at^2$$

• $$v = u + at$$

where:

• v$ is the final speed of the bike

• u$ is the initial speed of the bike (which is 0 in this case, since the bike starts from rest)

• a$ is the acceleration of the bike

• s$ is the distance traveled by the bike

• t$ is the time taken by the bike to travel the distance

Applying the Kinematic Equations

We can use the first kinematic equation to determine the acceleration of the bike. Rearranging the equation to solve for $a$, we get:

$$a = \frac{v^2 - u^2}{2s}$$

Substituting the given values, we get:

$$a = \frac{(7.10 \, \text{m/s})^2 - (0 \, \text{m/s})^2}{2(35.4 \, \text{m})}$$

Calculating the Acceleration

Now, let's calculate the acceleration of the bike using the equation above.

$$a = \frac{(7.10 \, \text{m/s})^2 - (0 \, \text{m/s})^2}{2(35.4 \, \text{m})}$$

$$a = \frac{50.61 \, \text{m}^2/\text{s}^2}{70.8 \, \text{m}}$$

$$a = 0.716 \, \text{m/s}^2$$

Conclusion

In this article, we have discussed how to determine the acceleration of a bike that accelerates uniformly from rest to a speed of $7.10 , \text{m/s}$ over a distance of $35.4 , \text{m}$. We have used the kinematic equations of motion to derive an equation for the acceleration of the bike, and then calculated the acceleration using the given values. The acceleration of the bike is found to be $0.716 , \text{m/s}^2$.

Additional Information

• Uniform Acceleration: Uniform acceleration is a type of motion where an object's speed changes at a constant rate.
• Kinematic Equations: The kinematic equations are a set of equations that describe the motion of an object under the influence of a constant acceleration.
• Acceleration: Acceleration is a measure of how quickly an object's speed changes.

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
  

Introduction

In our previous article, we discussed how to determine the acceleration of a bike that accelerates uniformly from rest to a speed of $7.10 , \text{m/s}$ over a distance of $35.4 , \text{m}$. In this article, we will answer some frequently asked questions related to uniform acceleration and the kinematic equations of motion.

Q&A

Q: What is uniform acceleration?

A: Uniform acceleration is a type of motion where an object's speed changes at a constant rate. This means that the acceleration of the object remains the same throughout the motion.

Q: What are the kinematic equations of motion?

A: The kinematic equations of motion are a set of equations that describe the motion of an object under the influence of a constant acceleration. The three main kinematic equations are:

• $$v^2 = u^2 + 2as$$

• $$s = ut + \frac{1}{2}at^2$$

• $$v = u + at$$

Q: How do I determine the acceleration of an object using the kinematic equations?

A: To determine the acceleration of an object, you can use the first kinematic equation:

$$a = \frac{v^2 - u^2}{2s}$$

Substitute the given values into the equation and solve for $a$.

Q: What is the difference between uniform acceleration and non-uniform acceleration?

A: Uniform acceleration is a type of motion where an object's speed changes at a constant rate, while non-uniform acceleration is a type of motion where an object's speed changes at a variable rate.

Q: Can I use the kinematic equations to determine the acceleration of an object if I know the initial and final speeds, but not the distance traveled?

A: Yes, you can use the second kinematic equation to determine the acceleration of an object if you know the initial and final speeds, but not the distance traveled:

$$s = ut + \frac{1}{2}at^2$$

Rearrange the equation to solve for $a$:

$$a = \frac{2s}{t^2} - \frac{2u}{t}$$

Substitute the given values into the equation and solve for $a$.

Q: Can I use the kinematic equations to determine the acceleration of an object if I know the initial speed, distance traveled, and time taken?

A: Yes, you can use the third kinematic equation to determine the acceleration of an object if you know the initial speed, distance traveled, and time taken:

$$v = u + at$$

Rearrange the equation to solve for $a$:

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

Substitute the given values into the equation and solve for $a$.

Conclusion

In this article, we have answered some frequently asked questions related to uniform acceleration and the kinematic equations of motion. We have discussed how to determine the acceleration of an object using the kinematic equations, and provided examples of how to use the equations to solve problems.

Additional Information

• Uniform Acceleration: Uniform acceleration is a type of motion where an object's speed changes at a constant rate.
• Kinematic Equations: The kinematic equations are a set of equations that describe the motion of an object under the influence of a constant acceleration.
• Acceleration: Acceleration is a measure of how quickly an object's speed changes.

References

• Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.