Which of the following best describes the relationship between an object's speed and its kinetic energy?

• A. Kinetic energy increases proportionally with the square of speed, as given by $K=\frac{1}{2}m{v}^2$.
• B. Kinetic energy decreases as speed increases.
• C. Kinetic energy increases linearly with speed.
• D. Kinetic energy is independent of speed.

Answer: (A)

Verified step by step guidance

1. Recall the formula for kinetic energy, which is given by \(K = \frac{1}{2} m v^{2}\), where \(K\) is kinetic energy, \(m\) is the mass of the object, and \(v\) is its speed.
2. Notice that in this formula, the speed \(v\) is squared, meaning kinetic energy depends on the square of the speed, not just the speed itself.
3. Understand that if the speed doubles, the kinetic energy increases by a factor of four (since \$2^{2} = 4$), showing a proportional relationship to the square of speed.
4. Compare this to a linear relationship, where kinetic energy would increase directly in proportion to speed, which is not the case here.
5. Conclude that kinetic energy increases proportionally with the square of the speed, as described by the formula \(K = \frac{1}{2} m v^{2}\).