# What happens to the kinetic energy of an object if we halve the velocity?

Dec 16, 2017

See below.

#### Explanation:

Kinetic energy is given by $K = \frac{1}{2} m {v}^{2}$

where $m$ is the mass of the object, and $v$ is the object's velocity (speed).

If we halve the object's velocity, we're saying that the final velocity is $\frac{1}{2}$ the initial velocity, or in symbolic terms, ${v}_{f} = \frac{1}{2} {v}_{i}$.

So, initially we would have ${K}_{i} = \frac{1}{2} m {v}_{i}^{2}$ and finally we would have:

${K}_{f} = \frac{1}{2} m {v}_{f}^{2}$

$= \frac{1}{2} m \cdot {\left(\frac{1}{2} {v}_{i}\right)}^{2}$

Note that the entire quantity—including both the $\frac{1}{2}$ and $v$ term—is squared.

$\implies \frac{1}{2} m \cdot \frac{1}{4} {v}_{i}^{2}$

Rearranging:

$\implies \frac{1}{4} \left(\frac{1}{2} m {v}_{i}^{2}\right)$

$= \frac{1}{4} {K}_{i}$

$\therefore$ We can see that the final kinetic energy of the object is $\frac{1}{4}$ of the kinetic energy initially possessed by the object.