Question:
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
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The motion is a body thrown up and returning under gravity; check each graph's slope and shape against \(x=ut-\frac12gt^2\).
Updated On: Nov 11, 2026
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The Correct Option is C
Solution and Explanation
The consistent motion is a vertical throw under gravity, going up and coming back to the start.
(1) velocity-time: straight line with negative slope \(-g\), crossing zero at the top. Correct.
(2) velocity-position: \(v^2=u^2-2gx\) gives a parabola with \(\pm v\) at \(x=0\) meeting at \(v=0\) at maximum height. Correct.
(4) position-time: \(x=ut-\frac12gt^2\) is an inverted parabola starting and ending at zero. Correct.
(3) distance-time: distance can never decrease or stay constant while the body is moving, and the initial slope should equal the initial speed \(u\neq0\). The graph starts with zero slope and flattens at the end, which is impossible for this motion. Incorrect.
Answer: (3)
(1) velocity-time: straight line with negative slope \(-g\), crossing zero at the top. Correct.
(2) velocity-position: \(v^2=u^2-2gx\) gives a parabola with \(\pm v\) at \(x=0\) meeting at \(v=0\) at maximum height. Correct.
(4) position-time: \(x=ut-\frac12gt^2\) is an inverted parabola starting and ending at zero. Correct.
(3) distance-time: distance can never decrease or stay constant while the body is moving, and the initial slope should equal the initial speed \(u\neq0\). The graph starts with zero slope and flattens at the end, which is impossible for this motion. Incorrect.
Answer: (3)
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