Question

A group of students experiments with an object that starts from a rest then moves with constant positive acceleration. As the object moves, the group measures several quantities about the object's motion. As part of their data analysis, the group plots pairs of quantities in an attempts to understand relationships between their measurements. In addition to plotting quantities that they directly measured, the group also plots manipulated versions of their measured quantities.
The group is ultimately able to describe several linear relationship between measured and manipulated quantities because several of the plots show straight-line trends. Three of the pairs of quantities listed below yield a straight-line graph for the group when plotted against each other.
Which one of the following option does NOT yield a straight-line graph when plotted?

• A. Time and Speed
• B. Displacement and $Spee{d}^2$
• C. Time and $Displacemen{t}^{\frac{1}{2}}$
• D. Speed and $Tim{e}^2$

Answer 1

The correct option is D Speed and $Tim{e}^2$

From equations of motion, we have,

$v=u+at=at$

$⟹\frac{v}{t}=a=constant$. Hence a straight line.

Also $s=ut+\frac{1}{2}a{t}^2=\frac{1}{2}a{t}^2$

$⟹\frac{s}{t^2}=\frac{a}{2}=constant$. Hence a straight line.

Also $v^2=2as$

$⟹\frac{v^2}{s}=2a=constant$. Hence a straight line.

Hence correct answer is option D.