# How does force relate to kinetic energy?

Mar 13, 2018

The force will determine how much energy the body will acquire.

#### Explanation:

From Newtons 1st law of motion, if a body is at rest and is subjected to a force which accelarates it at $a$ m/${s}^{2}$, then its velocity after t secs is:

$v = a \cdot t$

From Newtons 2nd law of motion, the Force required to accelerate a body is f=given by:

$F = m \cdot a$

The moving body will have a Kinetic Enery given by

$K . E = \left(\frac{1}{2}\right) \cdot m \cdot {v}^{2}$

Do some substitutions:
$K . E = \left(\frac{1}{2}\right) \cdot m \cdot {v}^{2}$

$\left(\frac{1}{2}\right) \cdot m \cdot {\left(a \cdot t\right)}^{2}$

$\left(\frac{1}{2}\right) \cdot m \cdot {a}^{2} \cdot {t}^{2}$

$\left(\frac{1}{2}\right) \cdot F \cdot a {t}^{2}$