An object starts from rest and moves with constant acceleration. Which pair of statements about its displacement graphs is correct?
ADisplacement vs. time is curved; displacement vs. time squared is a straight line
BDisplacement vs. time is a straight line; displacement vs. time squared is curved
CBoth displacement vs. time and displacement vs. time squared are straight lines
DBoth displacement vs. time and displacement vs. time squared are curved
Answer & Solution
Correct answer: A. Displacement vs. time is curved; displacement vs. time squared is a straight line
1. With constant acceleration from rest, displacement grows with the square of time.
2. Plotting displacement against time therefore traces a curve, not a straight line.
3. Plotting the same displacement against time squared straightens that curve into a line, since d is now proportional to t^2 directly.
_Source: OpenStax Physics (CC BY 4.0), Ch 3 "Acceleration", section 3.2 Representing Acceleration with Equations and Graphs_
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