A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

Motion in A Straight Line PYQ — JEE Main 2019 · 8 Apr · Shift 2 · Q48 with Solution

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Correct answer: D

A particle:

So acceleration is a positive constant: $a=\text{constant}>0$

Hence the standard equations are: $v=at$ $x=\frac12 at^2$ $v^2=2ax$

From the equations above:

$a$ vs $t$ graph must be a horizontal line above the time axis.
$v$ vs $t$ graph must be a straight line through the origin with positive slope.
$x$ vs $t$ graph must be a parabola opening upward, starting from the origin, with slope initially zero and increasing with time.
$v$ vs $x$ relation is $v=\sqrt{2ax}$ so it increases with $x$ but is not linear.

Since the options are combinations of figures labeled (A), (B), (C), (D), we identify which figure types can represent the above motion.

For uniformly accelerated motion from rest:

a correct figure could be a constant positive $a$ vs $t$ graph,
a correct figure could be a straight-line $v$ vs $t$ graph through origin,
a correct figure could be an upward-curving $x$ vs $t$ graph through origin,
an incorrect figure would be one that contradicts these relations (for example, a linear $x$ vs $t$ graph, or a curved $v$ vs $t$ , or anything inconsistent with starting from rest and uniform acceleration).

Thus the correct qualitative representations are (A), (B), and (D), while (C) is not consistent.

Given options:

Therefore the correct choice is: $\boxed{\text{D}}$

Stored correct answer: D

My derived answer: D

So they agree.