Question

draw a mass vs energy graph. draw a line for the 18 km/h speed. add a line to show what the graph would look like if the surfers were all traveling at a speed of 12 km/h instead. label each line and the axis variables. you do not need to add a scale to your axes.

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $E_k=\frac{1}{2}mv^{2}$, where $E_k$ is the kinetic energy, $m$ is the mass, and $v$ is the speed. For a constant speed $v$, the energy $E_k$ is directly proportional to the mass $m$. That is, $E_k = km$ (where $k=\frac{1}{2}v^{2}$ is a constant for a given speed).

Step2: For $v = 18\ km/h$

The equation for the energy - mass relationship is $E_{k1}=\frac{1}{2}m(18)^{2}= 162m$. This is a linear relationship of the form $y = mx$ (in our case, $E_{k1}$ is $y$, $162$ is the slope, and $m$ is $x$). On the graph, draw a straight line with a relatively steep slope and label it "Speed = 18 km/h". The x - axis is labeled "Mass (m)" and the y - axis is labeled "Energy ($E_k$)".

Step3: For $v = 12\ km/h$

The equation for the energy - mass relationship is $E_{k2}=\frac{1}{2}m(12)^{2}=72m$. This is also a linear relationship. Draw a straight line with a less - steep slope compared to the first line and label it "Speed = 12 km/h".

Answer:

Draw two straight - line graphs on a coordinate plane with the x - axis labeled "Mass" and the y - axis labeled "Energy". One line with a steeper slope labeled "Speed = 18 km/h" and another line with a less - steep slope labeled "Speed = 12 km/h".