To find the correct equation for calculating the kinetic energy of an object, let's evaluate each equation provided:
1. [tex]\( KE = mgh \)[/tex]
2. [tex]\( KE = \frac{1}{2} mv^2 \)[/tex]
3. [tex]\( KE = \frac{1}{2} at^2 \)[/tex]
4. [tex]\( KE = \frac{1}{4} g^2 \)[/tex]
We'll analyze each equation in the context of physical units and meanings:
1. [tex]\( KE = mgh \)[/tex]
- This equation represents the gravitational potential energy, not the kinetic energy. It is used to describe the potential energy of an object due to its height above the ground.
2. [tex]\( KE = \frac{1}{2} mv^2 \)[/tex]
- This is the correct formula for kinetic energy. Kinetic energy is the energy an object possesses due to its motion, and this equation accurately represents that, where [tex]\(m\)[/tex] is the mass of the object and [tex]\(v\)[/tex] is its velocity.
3. [tex]\( KE = \frac{1}{2} at^2 \)[/tex]
- This equation does not represent kinetic energy. It seems to mix the terms of acceleration ([tex]\(a\)[/tex]) and time ([tex]\(t\)[/tex]), which does not directly relate to energy.
4. [tex]\( KE = \frac{1}{4} g^2 \)[/tex]
- This equation is not physically meaningful in the context of kinetic energy. The term [tex]\(g\)[/tex] usually represents the acceleration due to gravity, and squaring it and multiplying by a constant does not correspond to the definition of kinetic energy.
Given our analysis, the correct equation for calculating the kinetic energy of an object is:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]
Thus, the correct formula is represented by option 2.
