Linearizing data Transitional Reasoning Practice

Questions

1. 1.

   A student investigates how the centripetal force $F$ acting on a toy car depends on its speed $v$ while moving in a horizontal circular track of known radius $r$. The theoretical relationship between these variables is given by $F = \frac{m}{r}v^2$, where $m$ is the mass of the car. To determine the mass of the car using linear regression, which combination of plotted variables and slope analysis should the student use?

   • A) Plot $F$ on the vertical axis and $v^2$ on the horizontal axis; calculate mass as $m = S \cdot r$, where $S$ is the slope.
   • B) Plot $F$ on the vertical axis and $v$ on the horizontal axis; calculate mass as $m = S \cdot r$, where $S$ is the slope.
   • C) Plot $F$ on the vertical axis and $v^2$ on the horizontal axis; calculate mass as $m = \frac{S}{r}$, where $S$ is the slope.
   • D) Plot $v^2$ on the vertical axis and $F$ on the horizontal axis; calculate mass as $m = S \cdot r$, where $S$ is the slope.

Answers and step-by-step solutions appear after you finish the test.