A Car Starts From Rest And Moves With A Uniform Acceleration Of $3 \, \text{m/s}^2$ For $20 \, \text{s}$. Calculate The Distance Covered At The End Of The Motion. A. 6 Km

**A Car Starts from Rest and Moves with a Uniform Acceleration: Calculating Distance Covered** ===========================================================

Introduction

In this article, we will explore the concept of uniform acceleration and its application in real-world scenarios. We will use a car as an example to calculate the distance covered at the end of a motion, given a uniform acceleration and time.

Understanding Uniform Acceleration

Uniform acceleration is a fundamental concept in physics that describes the rate of change of velocity of an object. It is a measure of how quickly an object's velocity changes over a given period of time. In this case, the car starts from rest and moves with a uniform acceleration of $3 \, \text{m/s}^2$ for $20 \, \text{s}$.

Calculating Distance Covered

To calculate the distance covered at the end of the motion, we can use the following formula:

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

where:

• $s$ is the distance covered
• $u$ is the initial velocity (which is 0 in this case, since the car starts from rest)
• $t$ is the time
• $a$ is the uniform acceleration

Plugging in the values, we get:

$$s = 0 \times 20 + \frac{1}{2} \times 3 \times 20^2$$

$$s = 0 + \frac{1}{2} \times 3 \times 400$$

$$s = 0 + 600$$

$$s = 600 \, \text{m}$$

Therefore, the distance covered at the end of the motion is $600 \, \text{m}$.

Q&A

Q: What is uniform acceleration?

A: Uniform acceleration is a measure of how quickly an object's velocity changes over a given period of time.

Q: How is uniform acceleration calculated?

A: Uniform acceleration is calculated using the formula $a = \frac{\Delta v}{\Delta t}$, where $a$ is the acceleration, $\Delta v$ is the change in velocity, and $\Delta t$ is the time over which the acceleration occurs.

Q: What is the formula for calculating distance covered under uniform acceleration?

A: The formula for calculating distance covered under uniform acceleration is $s = ut + \frac{1}{2}at^2$, where $s$ is the distance covered, $u$ is the initial velocity, $t$ is the time, and $a$ is the uniform acceleration.

Q: What is the distance covered at the end of the motion in this example?

A: The distance covered at the end of the motion is $600 \, \text{m}$.

Conclusion

In conclusion, uniform acceleration is a fundamental concept in physics that describes the rate of change of velocity of an object. We can use the formula $s = ut + \frac{1}{2}at^2$ to calculate the distance covered at the end of a motion, given a uniform acceleration and time. In this example, we calculated the distance covered at the end of the motion to be $600 \, \text{m}$.

Frequently Asked Questions

• What is the difference between uniform and non-uniform acceleration?
  • Uniform acceleration is a constant rate of change of velocity, while non-uniform acceleration is a variable rate of change of velocity.
• How is uniform acceleration related to the motion of an object?
  • Uniform acceleration is a measure of how quickly an object's velocity changes over a given period of time.
• What is the formula for calculating velocity under uniform acceleration?
  • The formula for calculating velocity under uniform acceleration is $v = u + at$, where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the uniform acceleration, and $t$ is the time.

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.