# What happens to the kinetic energy of a bus as it is braking?

Jan 23, 2018

Energy is always converted from one form to another.
The kinetic energy of a bus (or any other vehicle) is converted mainly into heat and sound by the break system.

#### Explanation:

$\setminus \Delta K = {K}_{\text{initial"-K_"final"="Dissipated Energy}}$

Example

A driver riding a ${10}^{4} \text{kg}$ bus, at $80 \text{km/h}$, steps on the brakes slowing the bus down to $60 \text{km/h}$. Evaluate the energy dissipated.

\Delta K=K_"initial"-K_"final"= (mv_"initial"^2) /2-(mv_"final"^2) /2=

m/2*(v_"initial"^2-v_"final"^2)=(10^4"kg")/2*[(80"km/h")^2-(60"km/h")^2].

Converting to SI units:

\Delta K=(10^4"kg")/2*[(22.2"m/s")^2-(16.7"m/s")^2]=5\times10^3"kg"*214"m"^2"/s"^2=1070 \times 10^3 "kg m"^2"/s"^2 = 1070 "kJ"