Question

how is kinetic energy calculated? *

ke= (1/2)mv

ke= ham

ke= mv^2

ke= (1/2)mv^2

Explanation:

Step1: Recall Kinetic Energy Formula

The formula for kinetic energy (KE) is derived from the work - energy theorem. Kinetic energy is the energy an object possesses due to its motion. The correct formula for kinetic energy is based on the mass (\(m\)) of the object and its velocity (\(v\)). The formula is \(KE=\frac{1}{2}mv^{2}\), where \(m\) is the mass of the object and \(v\) is the speed (magnitude of velocity) of the object.

Step2: Analyze Each Option

• Option 1: \(KE = \frac{1}{2}mv\) is incorrect because the velocity term should be squared according to the kinetic energy formula.
• Option 2: \(KE=h\times a\times m\) has no relation to the kinetic energy formula. The variables \(h\) and \(a\) are not part of the kinetic energy formula.
• Option 3: \(KE = mv^{2}\) is incorrect because it is missing the factor of \(\frac{1}{2}\) which is a part of the standard kinetic energy formula.
• Option 4: \(KE=\frac{1}{2}mv^{2}\) matches the correct formula for kinetic energy.

Answer:

D. \(KE = (1/2)mv^{\wedge}2\) (or in proper LaTeX notation \(KE=\frac{1}{2}mv^{2}\))