How does the object’s kinetic energy change?
MultipleChoice :
1) Halved.
2) Increased by a factor of nine.
3) Doubled.
4) There is not enough information to determine.
The correct answer and explanation is :
To determine how the object’s kinetic energy changes, we need more context. Specifically, we would need to know how the object’s speed or mass changes because the kinetic energy of an object depends on both its mass and the square of its velocity.
The formula for kinetic energy (KE) is:
[
KE = \frac{1}{2} m v^2
]
Where:
- (m) is the mass of the object,
- (v) is the velocity of the object.
Explanation:
- Halved: The kinetic energy would only be halved if the velocity of the object were reduced by a factor of ( \frac{1}{\sqrt{2}} ), or approximately 0.707 of its initial value.
- Increased by a factor of nine: The kinetic energy increases by the square of the velocity. If the velocity increases by a factor of 3, the kinetic energy will increase by a factor of ( 3^2 = 9 ). This is the correct choice if the velocity of the object is tripled.
- Doubled: The kinetic energy would be doubled if the velocity of the object were increased by a factor of ( \sqrt{2} ), or approximately 1.414. This would make the new kinetic energy twice the original value.
- There is not enough information to determine: This is true if the problem doesn’t specify how the mass or velocity of the object changes, and we can’t make a clear determination about the kinetic energy change.
Based on the provided options, the correct answer would depend on how the speed of the object changes. If the velocity is tripled, then the kinetic energy would increase by a factor of nine.
Therefore, the correct answer is:
2) Increased by a factor of nine.
This happens because kinetic energy depends on the square of the velocity, so if the velocity is increased by a factor of 3, the kinetic energy increases by ( 3^2 = 9 ).