Select the correct answer.

Which equation correctly relates kinetic energy, mass, and velocity?

A. [tex]KE=\frac{1}{2} m^2 v[/tex]
B. [tex]KE=\frac{1}{2} m v^2[/tex]
C. [tex]KE=\frac{1}{2} m v[/tex]
D. [tex]KE=\frac{1}{2} m v^3[/tex]



Answer :

Let's solve the problem step-by-step.

We need to identify the correct equation that relates kinetic energy ([tex]\( KE \)[/tex]), mass ([tex]\( m \)[/tex]), and velocity ([tex]\( v \)[/tex]).

The formula for kinetic energy is derived from the principles of physics, specifically from the work-energy theorem. For an object with mass [tex]\( m \)[/tex] moving with velocity [tex]\( v \)[/tex], the kinetic energy is mathematically given by:

[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]

Let's analyze the given options:

A. [tex]\( KE = \frac{1}{2} m^2 v \)[/tex]

Here, the mass [tex]\( m \)[/tex] is squared and the velocity [tex]\( v \)[/tex] is to the first power. This form is incorrect because kinetic energy does not involve mass squared, and velocity should be squared.

B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]

This matches our earlier stated formula for kinetic energy. The mass [tex]\( m \)[/tex] and the square of velocity [tex]\( v \)[/tex] are correctly included. Therefore, this looks like the correct option.

C. [tex]\( KE = \frac{1}{2} m v \)[/tex]

In this option, both mass [tex]\( m \)[/tex] and velocity [tex]\( v \)[/tex] are to the first power. This does not correctly represent kinetic energy because velocity should be squared, not to the first power.

D. [tex]\( KE = \frac{1}{2} m v^3 \)[/tex]

Here, the velocity [tex]\( v \)[/tex] is cubed. This is incorrect because kinetic energy involves the square of velocity, not the cube.

After reviewing all choices, the correct relationship is:

[tex]\[ \boxed{KE = \frac{1}{2} m v^2} \][/tex]

Therefore, the correct answer is:

B. [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]