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When the speed of a particle is increased 3 times, its kinetic energy:
- a)increases 3 times
- b)remains same
- c)increases 9 times
- d)decreases to 1/3.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When the speed of a particle is increased 3 times, its kinetic energy:...
The kinetic energy (KE) of a particle is a measure of the energy it possesses due to its motion. It is given by the following equation:
KE = 1/2 * m * v^2
where m is the mass of the particle and v is its speed.
If the speed of a particle is increased 3 times, its kinetic energy will also increase 3 times. This is because the speed is squared in the equation for kinetic energy, which means that any increase in speed will result in a much larger increase in kinetic energy. For example, if the speed of a particle is increased from v to 3v, the kinetic energy will increase from 1/2 * m * v^2 to 1/2 * m * (3v)^2 = 1/2 * m * 9v^2, which is 9 times the original value.
Therefore, if the speed of a particle is increased 3 times, its kinetic energy will increase 9 times.
Most Upvoted Answer
When the speed of a particle is increased 3 times, its kinetic energy:...
When the speed of a particle is increased 3 times, its kinetic energy increases 9 times. This relationship can be explained using the formula for kinetic energy.
The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
Where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.
Explanation:
1. Initial Kinetic Energy:
Let's assume the initial velocity of the particle is v1 and the initial kinetic energy is KE1. Using the formula, we can write:
KE1 = 1/2 * m * v1^2
2. Increased Velocity:
When the speed of the particle is increased 3 times, the new velocity becomes 3v1.
3. Final Kinetic Energy:
Let's calculate the final kinetic energy, KE2, using the new velocity:
KE2 = 1/2 * m * (3v1)^2
= 1/2 * m * 9v1^2
= 9 * (1/2 * m * v1^2)
= 9 * KE1
Conclusion:
Comparing the initial kinetic energy (KE1) with the final kinetic energy (KE2), we can see that the final kinetic energy is 9 times greater than the initial kinetic energy. Therefore, the correct answer is option C: the kinetic energy increases 9 times when the speed of a particle is increased 3 times.
The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
Where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.
Explanation:
1. Initial Kinetic Energy:
Let's assume the initial velocity of the particle is v1 and the initial kinetic energy is KE1. Using the formula, we can write:
KE1 = 1/2 * m * v1^2
2. Increased Velocity:
When the speed of the particle is increased 3 times, the new velocity becomes 3v1.
3. Final Kinetic Energy:
Let's calculate the final kinetic energy, KE2, using the new velocity:
KE2 = 1/2 * m * (3v1)^2
= 1/2 * m * 9v1^2
= 9 * (1/2 * m * v1^2)
= 9 * KE1
Conclusion:
Comparing the initial kinetic energy (KE1) with the final kinetic energy (KE2), we can see that the final kinetic energy is 9 times greater than the initial kinetic energy. Therefore, the correct answer is option C: the kinetic energy increases 9 times when the speed of a particle is increased 3 times.
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