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

Scatterplots

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, you probably know that the theoretical relationship between the variables is distance $$=490(time)^2.$$ Which of the following scatter-plots would not approximately follow a straight line?

(a) A plot of distance versus $$time^2$$

(b) A plot of radic distance versus time

(c) A plot of distance versus radic time

(d) A plot of $$\ln$$(distance) versus $$\ln(time)$$

(e) A plot of $$\log$$(distance) versus $$\log(time)$$

2021-06-24

Given:distance $$= 490(time)^2$$
(a) A plot of distance versus $$time^2$$ would approximately follow a straight line, because distance $$= 490(time)^2$$ and thus y $$= 490x$$ will be the straight line.
(b) A plot of sqrt(distance) versus time would approximately follow a straight line, because taking the square root of each side of distance $$= 490(time)^2$$ results in sqrt(distance) $$= \sqrt{490time}$$ and thus $$y = \sqrt{490x}$$ will be the straight line.
(c) A plot ofdistance versus sqrttime would not approximately follow a straight line, becatse distance $$= 490(time)$$? and thus there is a linear relationship between distance and $$(time)^2$$ but not between distance and sqrttime.
(d) A plot of In distance versus In time would approximately follow a straight line, because distance $$= 490(time)^2$$ is a power model (as we take the power of time) and we can straight the pattern in $$«$$ dotplot of a power model by taking the logarithm of each side.
(e) A plot of logdistance versus log time would approximately follow a straight line, because distance $$= 490(time)^2$$ is a power model (as we take the power of time) and we can straight the pattern in a dotplot of a power model by taking the logarithm of each side.