Question

which is the correct equation for calculating the kinetic energy of an object?
$ke = mgh$
$ke = \frac{1}{2}mv^2$
$ke = \frac{1}{2}at^2$
$ke = \frac{1}{4}g^2$

Explanation:

To determine the correct equation for kinetic energy (KE), we analyze each option:

• \( KE = mgh \): This is the formula for gravitational potential energy, where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height. So this is incorrect for kinetic energy.
• \( KE=\frac{1}{2}mv^{2} \): Kinetic energy depends on the mass (\( m \)) of the object and its velocity (\( v \)). The formula \( KE = \frac{1}{2}mv^{2} \) is the standard equation for calculating the kinetic energy of an object in motion.
• \( KE=\frac{1}{2}at^{2} \): This formula is related to the displacement in uniformly accelerated motion (\( s=\frac{1}{2}at^{2} \)) and not kinetic energy. So this is incorrect.
• \( KE=\frac{1}{4}g^{2} \): This formula does not involve mass or velocity (which are key for kinetic energy) and is not a valid kinetic energy formula.

Answer:

\( KE=\frac{1}{2}mv^{2} \) (the second option with the formula \( KE = \frac{1}{2}mv^{2} \))