Chapter 3, Problem 12STP

To determine

The relation between the car’s mass and its stopping distance.

Answer to Problem 12STP

The relation between the car’s mass and its stopping distance is linear relationship.

Explanation of Solution

Given info:

The table for car’s mass and stopping distance is shown below.

Car	Mass $\left(\text{kg}\right)$	Stopping Distance $\left(\text{m}\right)$
$\text{A}$	$1,000$	$80$
$\text{B}$	$1,250$	$100$
$\text{C}$	$1,500$	$120$
$\text{D}$	$2,000$	$160$

Calculation:

The relationship is linear relationship.The ratio between the mass of any two car’s is equal to the ratio between the stopping distance of that two cars.

For car A and B.

  $\begin{array}{c}\frac{\text{Mass}\text{of}\text{car}\text{A}}{\text{Mass}\text{of}\text{car}\text{B}}=\frac{\text{Stopping}\text{distance}\text{of}\text{car}\text{A}}{\text{Stopping}\text{distance}\text{of}\text{car}\text{B}}\\ \frac{1000}{1250}=\frac{80}{100}\\ 0\cdot 8=0\cdot 8\end{array}$

Conclusion:

Hence, the relation between the car’s mass and its stopping distance is linear relationship.