Which of the following variables directly determine the amount of kinetic energy an object has according to the formula $K=\frac{1}{2}m{v}^2$?

• A. Height and mass of the object
• B. Mass and speed of the object
• C. Acceleration and speed of the object
• D. Volume and density of the object

Answer: (B)

Verified step by step guidance

1. Recall the formula for kinetic energy: \(K = \frac{1}{2} m v^{2}\), where \(m\) is the mass of the object and \(v\) is its speed (or velocity magnitude).
2. Identify the variables in the formula: kinetic energy depends directly on the mass \(m\) and the square of the speed \(v^{2}\).
3. Understand that height, acceleration, volume, and density do not appear in the kinetic energy formula, so they do not directly determine kinetic energy.
4. Recognize that since kinetic energy depends on \(m\) and \(v\), changing either the mass or the speed will change the kinetic energy.
5. Therefore, the variables that directly determine the kinetic energy are the mass and the speed of the object.