College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 62

According to Physics, the Kinetic Energy $E$ of a moving object is joining proportional to the objects mass $m$ and the square of its speed $\nu$. A rock with mass 10kg that is moving and $\displaystyle 6 \frac{\text{m}}{\text{s}}$ has a kinetic energy of 180 Joules. What is the kinetic energy of a car with mass 1700 kg that is moving at $\displaystyle 30 \frac{\text{m}}{\text{s}}$

$\begin{equation} \begin{aligned} E &= k m \nu^2 && \text{Model}\\ \\ 180 \text{ Joules} &= k (10 \text{kg}) \left( 6 \frac{\text{m}}{\text{s}} \right)^2 && \text{Solve for } k \\ \\ k &= \frac{180 \text{ Joules}}{(10\text{kg})\left( 6 \frac{\text{m}}{\text{s}} \right)^2} \end{aligned} \end{equation}$

Thus, when $m = 1700$ kg and $\nu = 30 \frac{\text{m}}{\text{s}}$

$\begin{equation} \begin{aligned} E &= \frac{180 \text{ Joules}}{(10\text{kg})\left( 6 \frac{\text{m}}{\text{s}} \right)^2} (1700 \text{kg}) \left( 30 \frac{\text{m}}{\text{s}} \right)\\ \\ E &= 765,000 \text{ Joules} \end{aligned} \end{equation}$