To determine which equation correctly relates kinetic energy (KE), mass (m), and velocity (v), we need to consider the fundamental principles of physics.
The kinetic energy of an object is given by the equation:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Let's analyze each option to see which one matches this formula:
A. [tex]\( KE = \frac{1}{2} m^2 v \)[/tex]
- This equation says the kinetic energy is proportional to the square of the mass and linear in velocity, which is incorrect.
B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
- This equation shows the kinetic energy is proportional to the mass and to the square of the velocity, which matches our correct formula.
C. [tex]\( KE = \frac{1}{2} m v \)[/tex]
- This equation indicates that the kinetic energy is proportional to the mass and linear in velocity, which is incorrect.
D. [tex]\( KE = \frac{1}{2} m v^3 \)[/tex]
- This equation describes the kinetic energy as proportional to the mass and cubic in velocity, which is incorrect.
After carefully examining each option, we find that the correct relation between kinetic energy (KE), mass (m), and velocity (v) is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Therefore, the correct answer is:
B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
