# The kinetic energy of a particle of mass m is found by taking one half of the product of the mass...

## Question:

The kinetic energy of a particle of mass m is found by taking one half of the product of the mass and the square of the velocity. Write an expression for the kinetic energy of a particle.

## Algebraic equation word problems

An algebraic equation is formed when a relation between any variable is equated to a constant.

For example: 4x +3y = 1 is an algebraic equation where x and y are variables and 1 is the equivalent constant of the relation shown in the equation.

In the word problems of algebraic equation, this relation is given in statement and we need to form an algebraic equation out of it. Assuming a base variable and determining other unknowns in its term also helps in simplifying the equation.

Let the kinetic energy of a particle be {eq}K {/eq}, mass of the particle is {eq}m {/eq} and the velocity of the particle is {eq}v {/eq}

According to the problem statement: The kinetic energy of a particle of mass m is found by taking one half of the product of the mass and the square of the velocity.

$$Kinetic energy= \dfrac{1}{2}\times mass\times velocity^2$$

$$K= \dfrac{1}{2}\times m\times v^2$$

$$K= \dfrac{mv^2}{2}$$

The expression for kinetic energy is {eq}K= \dfrac{mv^2}{2} {/eq}