Given:- Mass, $m = 1.5 \, \text{kg}$- Kinetic Energy, $E_c = 500 \, \text{J}$Calculate The Velocity, $V$.$\[ V = \sqrt{\frac{2 \times E_c}{m}} \\]Substitute The Given Values:$\[ V = \sqrt{\frac{2 \times

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Understanding the Basics of Kinetic Energy and Velocity

Kinetic energy is a fundamental concept in physics that describes the energy an object possesses due to its motion. It is a measure of the work an object can do as it moves. The kinetic energy of an object is directly proportional to the square of its velocity. In this article, we will explore how to calculate the velocity of an object given its kinetic energy and mass.

The Formula for Kinetic Energy

The kinetic energy of an object is given by the formula:

Ec=12×m×V2{ E_c = \frac{1}{2} \times m \times V^2 }

where EcE_c is the kinetic energy, mm is the mass of the object, and VV is the velocity of the object.

Rearranging the Formula to Solve for Velocity

To solve for velocity, we need to rearrange the formula to isolate VV. We can do this by dividing both sides of the equation by mm and then taking the square root of both sides:

V=2×Ecm{ V = \sqrt{\frac{2 \times E_c}{m}} }

Given Values

We are given the following values:

  • Mass, m=1.5 kgm = 1.5 \, \text{kg}
  • Kinetic energy, Ec=500 JE_c = 500 \, \text{J}

Substituting the Given Values

Now that we have the formula and the given values, we can substitute the values into the formula to solve for velocity:

V=2×500 J1.5 kg{ V = \sqrt{\frac{2 \times 500 \, \text{J}}{1.5 \, \text{kg}}} }

Simplifying the Expression

To simplify the expression, we can first multiply the numerator and denominator by 2 to get rid of the fraction in the numerator:

V=1000 J1.5 kg{ V = \sqrt{\frac{1000 \, \text{J}}{1.5 \, \text{kg}}} }

Evaluating the Expression

Now we can evaluate the expression by taking the square root of the fraction:

V=1000 J1.5 kg=666.67 m2/s2{ V = \sqrt{\frac{1000 \, \text{J}}{1.5 \, \text{kg}}} = \sqrt{666.67 \, \text{m}^2/\text{s}^2} }

Calculating the Final Answer

Finally, we can calculate the final answer by taking the square root of the expression:

V=666.67 m2/s2=25.73 m/s{ V = \sqrt{666.67 \, \text{m}^2/\text{s}^2} = 25.73 \, \text{m/s} }

Conclusion

In this article, we have shown how to calculate the velocity of an object given its kinetic energy and mass. We have used the formula for kinetic energy and rearranged it to solve for velocity. We have then substituted the given values into the formula and simplified the expression to get the final answer. The final answer is V=25.73 m/sV = 25.73 \, \text{m/s}.

Additional Information

  • Kinetic energy is a measure of the work an object can do as it moves.
  • The kinetic energy of an object is directly proportional to the square of its velocity.
  • The formula for kinetic energy is Ec=12×m×V2E_c = \frac{1}{2} \times m \times V^2.
  • The formula for velocity is V=2×EcmV = \sqrt{\frac{2 \times E_c}{m}}.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers. Cengage Learning.
    Frequently Asked Questions (FAQs) about Calculating Velocity from Kinetic Energy =====================================================================================

Q: What is kinetic energy?

A: Kinetic energy is a measure of the energy an object possesses due to its motion. It is a measure of the work an object can do as it moves.

Q: What is the formula for kinetic energy?

A: The formula for kinetic energy is:

Ec=12×m×V2{ E_c = \frac{1}{2} \times m \times V^2 }

where EcE_c is the kinetic energy, mm is the mass of the object, and VV is the velocity of the object.

Q: How do I calculate velocity from kinetic energy?

A: To calculate velocity from kinetic energy, you need to rearrange the formula to isolate VV. You can do this by dividing both sides of the equation by mm and then taking the square root of both sides:

V=2×Ecm{ V = \sqrt{\frac{2 \times E_c}{m}} }

Q: What are the units of velocity?

A: The units of velocity are typically meters per second (m/s).

Q: Can I use this formula to calculate velocity for any object?

A: Yes, you can use this formula to calculate velocity for any object, as long as you know its mass and kinetic energy.

Q: What if I don't know the mass of the object?

A: If you don't know the mass of the object, you can't use this formula to calculate velocity. You need to know the mass of the object to use this formula.

Q: Can I use this formula to calculate kinetic energy from velocity?

A: Yes, you can use this formula to calculate kinetic energy from velocity. Simply rearrange the formula to isolate EcE_c:

Ec=12×m×V2{ E_c = \frac{1}{2} \times m \times V^2 }

Q: What if I have a negative value for kinetic energy?

A: If you have a negative value for kinetic energy, it means that the object is not moving. Kinetic energy is always positive or zero, so a negative value is not possible.

Q: Can I use this formula to calculate velocity for an object that is not moving?

A: No, you can't use this formula to calculate velocity for an object that is not moving. If the object is not moving, its kinetic energy is zero, and you can't use this formula.

Q: What if I have a non-zero value for mass but a zero value for kinetic energy?

A: If you have a non-zero value for mass but a zero value for kinetic energy, it means that the object is not moving. In this case, the velocity is also zero.

Conclusion

In this article, we have answered some frequently asked questions about calculating velocity from kinetic energy. We have covered topics such as the formula for kinetic energy, how to calculate velocity, and what to do if you don't know the mass of the object. We hope this article has been helpful in answering your questions about calculating velocity from kinetic energy.

Additional Information

  • Kinetic energy is a measure of the energy an object possesses due to its motion.
  • The formula for kinetic energy is Ec=12×m×V2E_c = \frac{1}{2} \times m \times V^2.
  • The formula for velocity is V=2×EcmV = \sqrt{\frac{2 \times E_c}{m}}.
  • Kinetic energy is always positive or zero, so a negative value is not possible.
  • If the object is not moving, its kinetic energy is zero, and you can't use this formula.