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

## Question:

The kinetic energy of a particle of mass {eq}M {/eq} is found by taking one-half of the product of the mass and the square of the velocity {eq}V {/eq}. Write an expression for the kinetic energy of a particle.

## Algebraic Expression

Writing algebraic expressions from statements of mathematics and physics problems is the first part of solving it. The correct operations and the extent thereof can only be written correctly if you understand the problem in the first place.

We will represent the kinetic energy of a particle as {eq}K.E. {/eq}, then let {eq}M {/eq} be its mass and {eq}V {/eq} be its velocity.

The statement says "one-half of" meaning the next values are all taken as a quantity and is divided into 2. The statement "the product of" means that the next values are multiplied, and "the square of" means that the next value is raised to 2. Writing the mathematical expressions should then be done from the last statement to the first and so we have:

{eq}\begin{align} K.E.= \dfrac{(MV^2)}{2}=\dfrac{1}{2}MV^2 \end{align} {/eq}