# Kinetic energy is calculated from the formula KE = \frac{1}{2}mv^2 Suppose a mass of 14.2 kg (m =...

## Question:

Kinetic energy is calculated from the formula {eq}KE = \frac{1}{2}mv^2 {/eq} Suppose a mass of 14.2 kg (m = 14.2 kg) is moving with a velocity of 750. m/s (v = 750. meters per second). Calculate the kinetic energy of this mass in units of Joules.

## Kinetic Energy:

The concept of energy, particularly kinetic energy, has vast implications in the motion and behavior of microscopic and macroscopic bodies. While it primarily describes the mechanical motion of an object, the kinetic energy of particles can also be related to several physical quantities of matter, such as temperature. Kinetic energy directly depends on two quantities: the mass and square of the velocity of the object/particle. Quantitatively, it is determined using the formula

$$KE = \frac{1}{2}mv^2$$

where:

{eq}m = \rm mass\ of\ object {/eq}

{eq}v = \rm velocity\ of\ object {/eq}

The SI unit of kinetic energy is in Joules (J), which is derived from the base units kilogram (kg) and meters per second (m/s).

From the formula

{eq}\rm KE = \rm \frac{1}{2} mv^2 {/eq}

the kinetic energy of an object with mass {eq}\rm m = \rm 14.2\ kg {/eq} and velocity {eq}\rm v = \rm 750\ m/s {/eq} is calculated to be

{eq}\begin{align} \rm KE &= \rm \frac{1}{2}mv^2\\ &= \rm \frac{1}{2}(14.2\ kg)(750\ m/s)^2\\ &= \rm (7.1\ kg)(5.63 \times 10^5\ m^2/s^2)\\ \rm KE &= \rm 3.99 \times 10^6\ J \end{align} {/eq}

Therefore, the kinetic energy of the mass is {eq}\boxed{\rm KE = \rm 3.99 \times 10^6\ J} {/eq}.