Sure, let's analyze each of the given equations and determine which one correctly represents the relationship between kinetic energy (KE), mass (m), and velocity (v).
1. Kinetic energy is related to mass and velocity by the formula for translational kinetic energy, which is derived from basic principles of physics.
2. The correct formula for kinetic energy is given by:
[tex]\[
KE = \frac{1}{2}mv^2
\][/tex]
Now, let's go through the options:
A. [tex]\( KE = \frac{1}{2} m^2 v \)[/tex]
- This equation suggests that kinetic energy is proportional to the square of the mass and linear to velocity. This is not correct because it should be mass times the square of the velocity.
B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
- This correctly represents the kinetic energy as it shows that kinetic energy is calculated as half the product of mass and the square of the velocity. This matches the established formula of kinetic energy.
C. [tex]\( KE = \frac{1}{2} m v \)[/tex]
- This equation indicates that kinetic energy is proportional to the mass and velocity, without the velocity being squared, which is incorrect.
D. [tex]\( KE = \frac{1}{2} m v^3 \)[/tex]
- This equation incorrectly suggests that kinetic energy is proportional to the mass and the cube of the velocity. This is not correct for kinetic energy.
After examining each option, the correct answer is:
B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]
