Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If

necessaryh

necessaryh

Answered question

2021-06-23

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 time2

(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)

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2021-06-24Added 91 answers

(a) A plot of distance versus time2 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) =490time and thus y=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.

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