Sure! The correct equation for calculating the kinetic energy (KE) of an object is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Let's break down why this is the correct equation.
1. Understanding Kinetic Energy:
- Kinetic energy is the energy that an object possesses due to its motion.
- The formula for kinetic energy is derived from the work-energy principle, where [tex]\( KE = (1/2) \times \text{mass} \times (\text{velocity})^2 \)[/tex].
2. Examining the Given Equations:
- [tex]\( KE = mgh \)[/tex]: This formula represents gravitational potential energy, not kinetic energy.
- [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]: This is the standard formula for kinetic energy.
- [tex]\( KE = \frac{1}{2} a t^2 \)[/tex]: This does not represent kinetic energy; it appears to incorrectly mix acceleration and time in a context not applicable to kinetic energy.
- [tex]\( KE = \frac{1}{4} g^2 \)[/tex]: This formula is not related to kinetic energy either; it involves gravity squared without any context.
3. Confirming the Correct Equation:
- The standard and widely accepted formula for kinetic energy is [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]. This matches one of the given equations.
Therefore, the correct equation for calculating the kinetic energy of an object is:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
This corresponds to the second equation in the list provided.
