Question

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance$=490{\left(time\right)}^2$. A scatterplot of the students’ data showed a clear curved pattern. A scatterplot of which of the following should have a roughly linear pattern?

(a) [time, ln(distance)]

(b) [ln(time), distance]

(c) [ln(time), ln(distance)]

(d) [ln(distance), time]

(e) [distance, ln(time)]

Short answer

A scatterplot that has a roughly linear pattern is option (c) [ln(time), ln(distance)] .

Step-by-step solution

Given information

Given in the question that, the theoretical relationship between the variables is the distance $=490{\left(time\right)}^2$.

Explanation

According to the result of exercise 47,

The transformations$\sqrt{dis\tan ce}$and ${\text{time}}^2$are are single transformations that linearize the connection.

The scatterplot will be about linear if you take the logarithm of both variables because the relationship is quadratic.