# Anna is riding a bicycle at a certain speed then stops pedaling and slows down to half of her...

## Question:

Anna is riding a bicycle at a certain speed then stops pedaling and slows down to half of her original speed. If the total kinetic energy of Anna and the bicycle was initially {eq}K_0 {/eq}, what was it after she slowed down?

## Kinetic Energy:

The kinetic energy is a very important parameter of an object in motion. If an object has a velocity {eq}v {/eq} and mass {eq}m {/eq} then the kinetic energy of the object is given by \begin{align} K=\dfrac12mv^2 \end{align}

This energy can be converted into another energy applying conservation of energy.

Let the bicycle has mass {eq}m {/eq} and velocity {eq}v {/eq}, then the kinetic energy is \begin{align} \boxed{K_0=\dfrac12mv^2} \end{align}

Now when it slows down to to the half velocity then the kinetic energy is \begin{align} &K'=\dfrac12m\left(\dfrac v2\right)^2\\[.3 cm] &K'=\dfrac14\times \dfrac12mv^2\\[.3 cm] &K'=\dfrac14\times K_0\\[.3 cm] &K'=\dfrac{K_0}4 \end{align}

Hence if the velocity is slowed down to half then the new kinetic energy is {eq}\dfrac{K_0}4 {/eq}. 